Unit 7 - HOMEWORK
Name: _______________________________________
Teacher: _______________________________________
Period: ____________
Lesson 1 – Understanding Percent Classwork
|State |Ratio of People Under 18 to |
| |Total Population |
|Arkansas |1 out of 4 |
|Hawaii |6 out of 25 |
|Mississippi |27 out of 100 |
|Utah |8 out of 25 |
Warm-up:
The table to the right shows the ratio of people under 18 years of age to the total population for various states.
1) Name two states from the table that have ratios in which the second numbers are the same.
_______________________________________
2) Of the two states you named in Exercise 1, which state has a greater ratio of people under 18 to total population? Explain.
____________________________________________________________________________________________________________________________________________________________________________________
3) Describe how to determine which of the four states has the greater ratio of people under 18 to total population.
____________________________________________________________________________________________________________________________________________________________________________________
Vocabulary:
Ratio: ___________________________________________________________________________________
Percent: _________________________________________________________________________________
Percent is ALWAYS out of _______!
Write each ratio as a percent:
|1) According to the 2000 U.S. Census, 26 out of every 100 people living in |2) At a recent triathlon, 80 women competed the triathlon for every 100 women who|
|Illinois were younger than 18. |competed ten years earlier. |
| | |
|3) During his baseball career, Babe Ruth had a base hit about 34 out of every 100|4) In a recent year, 94.5 out of 100 households in the United States had access |
|times he came to bat. |to the Internet. |
|5) About 1 out of 5 luxury cars manufactured in the United States is white. |6) About [pic]of travelers use scheduled buses. |
| | |
|7) In Finland, almost 4 out of 5 people have cell phone. |8) About [pic]of the mammals in the world are bats. |
| | |
Lesson 1 – Understanding Percent Classwork
Writing each percent as a fraction:
|The circle graph shows an estimate of the percent of each |
|type of trash in landfills. |
Write the percents for each of the following as a fraction in simplest form:
|Type of Trash |Percent |Fraction in |Percent as a Decimal |
| | |Simplest Form | |
|Paper | | | |
|Plastic | | | |
|Food and Yard Waste | | | |
|Other Trash | | | |
Practice with Understanding Percent:
I. Write each percent as a fraction in simplest form:
a) 29% b) 43% c) 40% d) 125%
e) 28% f) 64% g) 250% h) 4.5%
II. Write each percent as a decimal:
a) 50% b) 25% c) .40% d) 75%
e) 15% f) 2.8% g) 85% h) 1.25%
III. Critical Thinking
a) Which has a lesser value and why? [pic] or 30%
b) Explain how a student can receive an 86% on a test with 50 questions.
__________________________________________________________________________________________
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Understanding Percent Lesson 1 – Homework
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|1A) What is 80% of 75? |1B) What is 80% of 75? |
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|2A) 6% of 150 is what number? |2B) 6% of 150 is what number? |
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|3A) 60 is 80% of what number? |3B) 60 is 80% of what number? |
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|4A) 99 is 180% of what number? |4B) 99 is 180% of what number? |
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|5A) 25 is what percent of 150? |5B) 25 is what percent of 150? |
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|6A) 60 is what percent of 75? |6B) 60 is what percent of 75? |
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[pic] OR [pic] or Equation
[pic]. Nick answered 90% of the questions on his math correctly. If he answered 45 of the questions correctly how many questions were on the test?
_________________________________________________________________________________________
8. The Jets played 8 games. If they lost 2, and there were no ties, what percent of the games did they WIN?
__________________________________________________________________________________________
9. Of the 200 bicycles at a vacation resort, 40 are NOT yet rented.
a. What percent are not rented?
b. What percent are rented?
__________________________________________________________________________________________
10. There are 330 seventh graders at Seneca Middle School. The number of seventh graders is 30% of the number of students enrolled in the school. How many students are enrolled at Seneca?
__________________________________________________________________________________________
11. Mr. DeMeo has 50 CD’s. 28 are rap, 22 are rock. What percent of Mr. DeMeo’s CD’s are rock?
Three Cases of Percent Homework Day 2
1) What is 63% of 300 2) 52.3 is what percent of 1046? 3) 13 is 50% of what number?
4) What is 18% of 650? 5) 11 is 4% of what number? 6) 0.4 is what percent of 5?
7) Of the 300 7th graders at Seneca, 96 have made honor roll. What percent of students made honor role?
8) A Volleyball team won 2 games and lost 6 games. What percent did they win?
9) Dylan received a bonus that is 40% of the monthly salary. If his monthly salary is $800, how much was his
bonus?
10) Nikki got 70% of the questions on a math test correct. The test had 50 questions. How many questions did
Nikki get correct?
11) Of the 300 golf clubs Jane has at her miniature golf stand, 60 are being used. What percent of the golf
clubs are not being used?
12) In Disney World there are a total of 50 mini boat rentals. If 46 are rented, what percent are not rented?
13) Of the 20 CDs that Thomas has 15 are rap and the rest are rock. What percent are rock?
14) Simplify: [pic] 15) Simplify: [pic]
Lesson 3 – Working with Mental Percent Classwork Day 3
Vocabulary:
Percent: ___________________________________________________________
Estimate: __________________________________________________________
Mental Math in Percent Problems:
1. 10% of 75 2. 10% of 300 3. 10% of 450
4. 10% of 18 5. 10% of 750 6. 10% of 6,600
7. 5% of 60 8. 5% of 200 9. 5% of 40
|13. What is 10% of 60? |14. 20% of 80 |15. 40% of 70 |
|16. 5% of 200 |17. 60% of 820 |18. 10% of 60 |
|19. 30% of 30 |20. 40% of 90 |21. 75% of 80 |
10. 5% of 100 11. 5% of 90 12. 5% of 1,200
Lesson 3 – Working with Mental Percent Classwork Day 3
Estimation: What if we aren’t working with 5%, 10% or 20%? In these cases, ESTIMATE!
Example: Find 22.8% of 162.
Practice:
1. 32% of 34 2. 17% of 942 3. 11% of 98
4. At a grocery store, four items cost $3.94, $7.11, $6.87, and $21.03. Estimate the total cost of these items.
5. The Yankees had 57,435 fans at the stadium. Of those fans, 81% of them were actually rooting for the Yankees. Estimate how many fans were rooting for the Yankees.
6. Gabriella decides to buy a car for $28,945, a computer for $1,189 and a HDTV for $2,206. Estimate the total cost of Gabriella’s purchases.
7. There are 1,289 students enrolled at Seneca. 38% of the students are in seventh grade. Estimate how many students are seventh graders.
Lesson 3 – Working with Mental Percent Homework Day 3
Using mental math, determine the following.
1. 10% of $85.00 2. 5% of 40 3. 20% of 40 4. 50% of 200
Determine the best estimate.
4. 27.8% of 462 5. 21% of 29 6. 33.3% of 85
7. Joe had 119 catches this year. If 19% of his catches are touchdowns, about how many touchdowns does he have?
8. Kristina took a test that had 50 questions. She got 78% of them correct. About how many questions were right?
9. Caitlyn went shopping for the holidays and purchased jeans for $45.75, a sweater for $36.20, and a hat and scarf for $18.35. She had a 20% off coupon. Estimate how much she saved off her total cost.
Review:
10) Solve: [pic] 11) Simplify: 2+3(x – 4) + 7x 12) Solve: [pic]
13) It took a submarine 20 seconds to drop to 100 feet below sea level from the surface. What was the rate of the descent?
14) Ashley thinks the two expressions 2(3a - 2) + 4a and 10a - 2 are equivalent? Is she correct? Explain why or why not?
Lesson 4 – Tax and Tip Classwork Day 4
Tax – Add to the original price for the total cost.
Tip – Add to the original bill for the total cost.
Money is always two decimal places (rounded to the nearest hundredth)
Example:
1) Sally just bought the new iPad Mini. It was $459 plus 8% sales tax. How much was her total purchase?
There are two ways to solve this problem
Method 1:
Find out what is 8% of $459
–––––– = ––––––
Then add it to the original
Item price + Tax = Grand total
_________ + _________ =
2) A sweatshirt at Hollister costs $60, the rate of tax is 9%. How much will the sweatshirt cost with tax?
Find the tax: Find the grand total:
3) After eating lunch at Chilli’s, the cost of the two meals are $35. If you want to leave a 20% tip, how much money should you leave altogether?
3) A 52 inch HD flat screen TV costs $1600. If the tax is 8.5%, how much will the TV cost all together?
4) Tom’s bill at a restaurant was $29.15. He plans to leave a 15% tip for the waiter.
Explain how Tom can ESTIMATE the amount for the tip.
5) At a discount store, Chris offered a salesperson $600 for a couch. This offer includes the 8% sales tax. If the
salesperson accepts the offer, what would be the price of the furniture, to the nearest dollar, before tax?
6) Mr. DeMeo goes on a jet skiing tour while on vacation. The company charges $199 and 6.25% in tax. After
the tour, he gives the instructor a 15% tip on his debit card. How much did the whole excursion cost?
Tax and Tip Day 4 – Homework
**Reminder: Find the tip based on the original bill**
1) Patti works at a restaurant. She usually makes 15% tips on all the sales she makes for the night.
If she had $784 in meals, estimate how much she could make in tips.
3) Terry wants to buy a Wii, but he is unsure if he has enough money. The Wii costs $300 and there is
a 9% sales tax on it. If he has $325 does he have enough money?
4) Lowes charges $1.80 for a 10-foot board, plus 5% for preparation cost.
a) If you need 50 boards, how much would the preparation cost be for all 50?
b) What would the total cost be for all 50?
5) You and a friend go out for dinner and spend $77.16. You want to leave a 15% tip. Your friend tells to
leave $20. Is he right? Explain. How would you do this problem in your head?
6) A new phone costs $399.00, if tax is 7.5%, what is the total cost of the phone?
7) Bryce bought an aquarium priced at $90.70. Shipping and handling cost him an additional 20%.
What was the total cost of the aquarium, including shipping and handling?
8) Lynda was a horrible waitress. She spilled a drink on you and she brought you the wrong food.
The bill came to $56.35 so you left her $3. What was the percent of tip you left her?
9) Sancho and his friend went to dinner at Applebee’s. Their meal cost them $27. Tax was 9% and they left
an 18% tip. What was the grand total Sancho charged to his credit card?
Day 5 – Commission Classwork Day 5
Commission – Add to the your base salary to get the total salary.
**Think of commission as a tip from your job**
If you earn 3% of what you sell, simply multiply your total sales by 0.03.
This will give you the amount you receive.
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1) Mrs. Dragotta works at Game Stop in her spare time. She earns an 8% commission for all sales.
She sold $1500 in the month of November.
a) What was her commission?
b) If Mrs. Dragotta makes $300 per week base plus commission, how much did she earn in November?
2) Mr. DeMeo sells 12 CD’s on ebay for $120. He gets a check for only $84 after the commission. Find the
commission percent charged by the site?
3) Kent is a real estate agent. He gets 2.5% commission on each house he sells.
a) Find the commission Kent gets if he sells a house for $340,000.
b) The day of the sale, Kent made a total of $10,000. How much of his salary did not include the
commission from selling the house?
Try These:
1) Eric gets a 7% commission for each electronics item he sells. If he sells $3000 worth of electronics,
how much commission does he make?
2) Your Uncle is having a garage sale and asks you to come work it for him. You strike a deal for 3% of whatever you can sell. If you so two TVs for $60 each and a blow dryer for $12, how much commission does do you make? How much money does your uncle walk away with?
Day 5 – Commission Classwork Day 5
3) A real estate agent sells condos for $90,000 each. She earns a 4% commission. In May, she sold 9 condos.
a) How much commission does she make on each condo?
b) How much in commission did she receive in May?
4) Mandy’s monthly earning consist of a fixed salary of $2800 and an 18% commission on all of her monthly sales. To cover her planned expenses, Mandy needs to earn an income of at least $6400 this month.
a) Write an inequality, that when solved, will give the amount of sales Mandy needs to cover her
planned expenses for the month.
b) Graph the solution of the inequality on the number line below.
Challenge
5) While on vacation in Spain, a group can rent bicycles and scooter by the week. They get a reduced rental rate
if they rent 5 bicycles for every 2 scooters rented. They reduced rate per bicycle is $15.50 per week and the reduced rate per scooter is $160 per week. The sales tax on each rental is 12%.
a) The group has $1600 available to spend on bicycle and scooter rentals. What is the greatest number of bicycles and the greatest number of scooters the group can rent if the ratio of bicycles to scooters is 5:2?
b) If they do rent the greatest possible amount for each, they sales clerk will earn a 7% commission of the final price. What will the commission be?
Commission Homework Day 5
1) If Drew’s sales for one week totaled $ 1500, and his commission on those sales totaled $82.50, then what is
the percent of commission he received?
2) Luke is paid a 10% commission on his sales of $2300. He also made an additional bonus of 2% this month
on those same sales. How much combined commission was earned?
3) Renee works in the shoe department at Saks 5th Ave and has a salary that includes a base and a commission
of 11% on all sales. If Renee makes $200 per week plus commission, how much does she make if she sold $6,500 worth of shoes? (Base + Commission : Total Salary)
4) Robbie, a car salesman at KIA, makes 4% commission on all sales. He sells 5 cars for $15,000 each.
What was his total commission on his sales?
5) What is the commission percentage paid on a $450 diamond necklace if you make $50?
6) Will is a real estate agent. When he sells a house he gets 3% and if they buyers are his customers too, then he
gets another 3%. How much money will he receive, if he sells the house for $345,000 to his customers?
7) Mario sells ovens at Lowes. He earns 5.6% commission on each oven sold. Today, he sold an oven for
$1190. How much commission did he earn?
8) EBay charges a commission of 18% if the item sells for $500 or less. If the item sells for more than
$500 it charges 18% for the first $500 and 9% on the amount over $500.
a) Find the commission for a $400 sale
b) Find the commission on a $650 sale.
Lesson 6 – Discount Classwork Day 6
Steps:
1) Find the discount, by setting up a proportion.
2) Subtract the discount from the original price…this will give you the SALES PRICE.
3) Find the tax if necessary, by setting up a proportion.
4) Add the tax to the SALES PRICE, this will give you the final cost.
Example:
You are buying a pair of sweats from Abercrombie & Fitch for $50.
They are on sale for 20% off.
20% off means that you are paying 80% of the total cost.
100% - 20% = 80%
So, to find the sale price, you multiply the cost by the percentage you are paying
$50 • 80% ( 50 • .80 = 40
The sale price of the sweatpants is $40.
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1) A Blu Ray Disc player has a list price of $350 and is discounted 25%.
a) How much would the savings be? (discount) b) What is the sales price?
c) If the tax is 8%, how much tax should they pay? d) What is the total cost of the DVD player?
2) A Twilight DVD costs $19.90. If you saved 30% off the original price, how much does the DVD now cost?
3) Aéropostale is having a sale on jeans. The original price was $49.50. The sale price is $33.00.
What percent discount was taken? (percent of decrease)
4) A comforter at Bed Bath & Beyond is $99 and you have a 15% off coupon. The same comforter is $99 at JC Penny’s but is on sale for 10% off. You also have a coupon for 5% off your total purchase at JC Penny’s. Which is better deal?
Lesson – Discount Classwork Day 6
5) A coat is currently $139.99. It is going on sale for 30% off.
a) How much would you save? b) What will the new cost of the coat be?
c) If 6 % sales tax is now added, what is the final cost?
6) You find sneakers for $79.95 at Modell’s. In the paper, you see they will be on sale for $63.96 next week.
a) What is the percent of discount that they will be offering?
b) If you wait and buy them next week, you will also have a coupon for an additional 15% off your
purchase. How much will the shoes cost you?
7) Ryan buys a 3-D HDTV for his brother while it was on sale for 15% off. The TV originally cost $2350.00.
What is the sale price?
8) An XM radio player that lists for $398 in on sale for 30% off the list price. How much money do you save?
9) A Skateboard is reduced 25% in price in a sale. The old price was $120. Find the new price
Discount Homework Day 6
1) A Laptop is on sale for 20% off the regular price. The price was originally $879.00. What is the sale price?
2) A washing machine is on sale for 15% off of the list price of $620.
a) What would the cost be after the savings?
b) What would be the final cost of the machine after tax of 8.25% is applied?
3) This year the price of a gallon of gasoline dropped from $4.25 a gallon to $3.69 a gallon.
Find the percent of discount to the nearest tenth?
4) A television on sale for 40% off saves you $184. What is the original price of the television? What is the sale price (before tax)?
5) Last year there were 260 7th graders at Seneca. This year the number of students decreased
by 5%. How many less students are there? What is the new size of the 7th grade class?
6) Ben wants to buy a stereo. The regular price of the stereo is $420. The sale Best Buy is having says you can
get $25 off for every $100 worth of merchandise purchased. He also has a coupon 25% off of the regular price.
a) What is the sale price of the stereo?
b) What is the price of the coupon if he used the coupon instead?
c) Ben must pay 7.25% sales tax in addition to the lower price of the stereo. What is the total amount Ben must pay for the stereo?
Lesson 7 – Deconstructing/Rewriting Expressions Classwork Day 7
Tax and Tip
Mary buys $75 coat that has 8% tax. What is the final price of the coat?
Since it is asking for the final price you are paying 100% for the coat
+ 8% for tax
That means you are paying 108%
You must now change the percent to a decimal ( 108 % = 1.08
Take the coat price and multiply by the decimal ( 75 (1.08)
Your final price is $81
Examples:
1) A book at Barnes and Nobles cost $40 with 8% tax. Find the final price.
2) Michelle purchased a cd which was selling for $15. The tax was 7%. How much was the total cost?
3) Emily and her friends went to dinner and left a 5% tip for her waitress. If her bill was $25.00, how much did they pay in total?
4) A small business buys a computer system for $850 and pays a sales tax that is 5% of the cost. What is the final cost of the computer system?
5) Lori bought a turtle for $8.00, two goldfish for $1.00 each, and a snail for $0.50. There was 8.5% tax. What is the final cost at the store?
6) Ashley and her family went out to dinner. Their bill came to $40.00. If Ashley’s dad would
like to leave a 20% tip and there is 8% tax, how much was their whole bill?
7) A dinner costs $60.75. There was 7.5% tax and the family wanted to leave a 15% tip. How much was the
final bill?
Lesson 7 – Deconstructing/Rewriting Expressions Classwork Day 7
Discount:
You are buying a pair of sweats from Abercrombie & Fitch for $50.
They are on sale for 20% off.
20% off means that you are paying 80% of the total cost.
100% - 20% = 80%
You must now change the percent to a decimal ( 80 % = 0.80
So, to find the sale price, you multiply the cost by the percentage you are paying
50 • 0 .80 = 40
The sale price of the sweatpants is $40.
1) The list price on a winter coat is $60. It is being sold at a 25% discount. What is the final price of the coat?
2) The regular price of an iPod is $480. It is on sale at a 35% discount. What is the sale price of the iPod?
3) A $135 snowboard was sold for 10% off. What was the total cost of the snowboard?
4) A Sweatshirt normally costs $22. This week it is on sale for 25% off the original price. What is the sale price of the sweatshirt?
5) A cowboy hat is regularly priced at $42. It is on sale for 15% off of the regular price. What is the final price?
*** Challenge***
6) A bottle of lotion is $25. The lotion is 20% off but you must pay 8% tax. What is the final price?
Lesson 7 – Deconstructing/Rewriting Expressions Homework Day 7
Using the deconstructing method solve each problem:
1) A customer wants to tip 15% on a restaurant bill that is $35. What will be the total bill with
tip?
2) Mark wants to buy exercise equipment that costs $140 and the sales tax is 8.5%. What is the
total cost of equipment?
3) Emily is buying a Bike. The total for the Bike is $240. Emily has a 30% off coupon. How
much is the sale price?
4) Ryan wants to tip his taxicab driver 20%. If his commute costs $15, what is the total cost?
5) Find the total cost of a spa treatment of $42 including 6% tax and 20% tip.
**** Challenge****
6) Melissa bought a $120 necklace. She used a 20% off coupon and had to pay 7% tax. What
was her final total of the necklace?
7) When you have a commission question and you decide to use the deconstruction method to solve it why would you always get a decimal with no whole number 1. (example 0.25). Explain why a commission question doesn’t start with 100%.
______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Lesson 8 – Percent of Change Classwork Day 8
Memorize the following proportion: This formula is used when you have:
*Percent of Increase
*Percent of Decrease
*Percent of Discount
Find the percent of change round to the nearest tenth if necessary:
1) From $50 to $67 2) From 45 in. to 18 in. 3) From 80 cm to 55 cm
Original :____
New :____
Difference:____
4. Your friend diets and goes from 125 pounds to 110 pounds. What was her percentage weight loss?
5. Eric bought a sweatshirt from Hollister for $30. If it originally cost $40, what was his percent of discount?
(round to the nearest percent)
6. In last week’s game, the basketball team scored 30 points. This week they scored 24 points. What percent
of last week’s score was the decrease?
7. In the past, Lexi got paid $80,000 annually. Since switching to a new career, she has been making $100,000
annually. What was the percent of increase in Lexi's pay?
Try these:
1) Shannon is selling some embroidered jackets on a Web site. She wants to price the jackets 25% over her cost,
which is $35. Find the selling price for a jacket.
2) At a supermarket, a certain item has increased from 75 cents per pound to 81 cents per pound.
What is the percent markup in the cost of the item
3) What is the markup rate on a $230 game system that sells for $345?
Lesson 8 – Percent of Change Classwork Day 8
4) In 2000, there were 365 endangered species in the US. One year later, 367 species were considered
endangered. What was the percent of change?
5) Suppose 36 videos are added to a video collection that has 24 videos. What is the percent of change?
6) Suzy swam 50 laps on Wednesday and 45 laps on Friday. What was the percent of decrease?
7) Alison earned $40 last week babysitting. This week she earned $50. What was her percent of increase?
8) Eric bought a sweatshirt from Hollister for $30. If it originally cost $40 what was his percent of discount?
9) In the US during the 20th century, average life expectancy increased from about 50 years to about 75 years.
Find the percent of increase.
10) According to his running log, Fidel averaged 4 miles per day last week and 50% less this week.
How much did he average this week?
11) In an effort to protect the environment, Serena is trying to get the citizens of her hometown, South Plains, to waste less water. A study indicated that they wasted 50,000 gallons of water last year and 30,000 gallons of water this year. What is the percent of decrease in the amount of water wasted yearly?
Homework Lesson 4 – Percent of Change
1. Best Buy decreased the cost of a Sony flat screen monitor from $525 to $430. What is the percent of
decrease?
_____________________________________________________________________________________
2. Brandon swam 50 laps on Wednesday and 55 laps on Friday. The increase is what percent of
Wednesday’s laps?
_____________________________________________________________________________________
3. Find the selling price for a $700 computer if the store has a 30% markup rate.
_____________________________________________________________________________________
4. Write a percent of increase problem where the percent of increase is greater than 100%.
______________________________________________________________________________________
5. Jared and Sydney are solving the following problem. The price of a movie ticket rose from $5.75 to $6.25. What is the percent of increase for the price of a ticket? Who is correct? Explain.
__________________________________
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__________________________________
__________________________________
__________________________________
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6. Bicycle Bob rented 60 bikes on Saturday, and 180 bikes on Sunday.
a. What is the percent increase of bikes rented?
b. What might account for the increase in rentals on Sunday?
Review:
7. Simplify: -2(4x – 0.5) + 3x 8. Find the unit price: 6 bananas for $4.68 9. Solve: 0.2(20x – 40) = 122
Lesson 9 – Percent Error Classwork Day 9
Vocabulary:
Relative Error: _____________________________________________________________
Percent Error: ______________________________________________________________
1. Joshua uses his thermometer and finds the boiling point of ethyl alcohol to be 75o C. He looks in a reference book and finds that the actual boiling point of ethyl alcohol is 80oC. What is the relative error? What is his percent error?
2. The density of water at 4oC is known to be 1.00 g/mL. Kayla experimentally found the density of water to be 1.075 g/mL. What is the relative error? What is her percent error?
3. The Handbook of Chemistry and Physics lists the density of a certain liquid to be 0.7988 g/mL. Taylor experimentally finds this liquid to have a density of 0.7925 g/mL. The teacher allows up to +/- 0.5% error to make an “A” on the lab. Did Fred make an “A”? Prove your answer.
4. An object has a mass of 35.0 grams. On Anthony’s balance, it weighs 34.85 grams. What is the percent error of his balance?
5. What is the percent error in using 3.14 as an approximation for π (which is 3.14159265358979323846...) ?
Percent Error Homework Day 9
1) A dairy sells milk in gallon containers. The containers are filled by machine and the amount of milk may vary slightly. A quality control employee selects a container at random and measures of the amount of milk as 16.25 cups. Find the percent of error to the nearest tenth of a percent.
2) The true length of the diagonal of a 13 by 84 rectangle is 85. Sarah drew a 13 by 84 rectangle and measured the diagonal to be 86. Find, to the nearest hundredth, her relative error.
3) Eli bought new carpet for his living room. He calculated the area of the living room to be 174.2 square feet. The actual area was 149.6 square feet. What is the relative error of the area to the nearest ten-thousandth?
4) A carpenter measures the length of a board as 50.5 centimeters. The actual measure of the length was 50.1 centimeters. Find the relative error in the carpenter’s measure to the nearest thousandth.
5) To calculate the area of her rectangular garden, Jill measured the length as 8 feet and the width to be 5 feet. The actual length of the garden is 8.2 feet by 4.7 feet. What is the percent of error in her area calculation to the nearest hundredth?
Lesson 10 – Simple Interest Classwork Day 10
Interest = (principal)(rate)(time)
Steps:
1) Change the rate (%) to a decimal.
2) Make sure the time is in years.
3) Write I=, P=, R=, T=
4) Substitute each value into the equation (with PARENTHESIS)
5) Solve.
p is the principle. The money borrowed or invested.
r is rate. Rate is a percentage. You must change the percent to a decimal to solve the problem.
t is time. Time is in years. If it is in months, you must convert it to years to solve the problem.
1) Change each percent to a decimal
A) 24% B) 159% C) 8.4% D) 0.56% E) [pic]%
2) Change months to years
A) 6 months B) 9 months C) 18 months D) 24 months
3) Mrs. Cohen deposited $200 in a bank that pay’s 5% simple interest. How much will she earn in three years?
4) Suzy invested $500 at 8% simple interest.
a) What does the investment pay in 6 months? b) How much total money does she now have?
5) If you buy a car for $19,000 at an interest rate of 4.5% for 5 years, how much are you actually paying for the car?
6) If you buy a car for $20,000 at an interest rate of 3% for 5 years, what is the simple interest?
7) You invest $1,500 for three years. Find the amount of simple interest you earn at an annual rate of 6.25%?
*8) Suppose you invested $1200 for four years. You earned $312 in simple interest. What is the interest rate?
9) If you buy a house for $525,000 at an interest rate of 7% for 15 years, how much are you actually paying for
that house?
Simple Interest Lesson 10 – Homework
1) What is a reasonable estimate of the amount of money you will earn on $595 invested at 9% simple interest for 2 years?
2) Explain whether you would earn more money from Plan A or Plan B.
Plan A: $1,500 for 7 years at 8% Plan B: $1,500 for 8 years at 6%
3) Connor agreed to pay back a loan in 3 years at a simple interest rate of 15% on $2500 he borrowed.
What is the total he must pay back?
4) Taylor borrowed $1200 at a simple interest rate of 8.5% for 6 months. How much interest did she owe?
5) $895 was invested for 2 years at 10% interest. How much total money do you have after the 2 years?
6) How much money is earned if $50 is invested at 17.5% simple interest for 2 years?
7) What would you have to repay if you borrowed $700 at simple interest for 3 years at 6%?
8) What is the interest if $4500 is borrowed at 9.5% simple interest for 2 years 6 months?
9) Courtney borrowed $500 from the bank. She was charged her 9% interest per year. The loan was for 2 years,
how much does she have to pay?
*10) Sydney borrowed $1200 at a simple interest rate for 6 months. If the interest was $51 what was the rate of interest?
Extended Response:
11) If you buy a house for $450,000 at an interest rate of 6% for 30 years.
a) What is the interest?
b) How much will you actually be paying for the house?
c) What will your monthly payment be?
d) How much money would you save if you took out the loan for 15 years?
e) Why might a person take out a 30 year loan instead of a 15 year loan?
Lesson 11 – Two-Way Frequency Table (Bivariate data) Classwork Day 11
Vocabulary:
Relative Frequency Table – _____________________________________________________________
Relative Frequency Tables can be created: 1) ________________
2) ________________
3) ________________
1) Fifty students in the 8th grade class were asked what kind of ice-cream they like (vanilla or chocolate) and
|Topping |Sprinkles |m & m’s |Nothing |Total |
|Chocolate |7 |9 |4 |20 |
|Total |16 |17 |17 |50 |
what kind of toppings they like (sprinkles, m & m’s, or nothing). Identify any trends in the data.
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
2) To create a relative-frequency two way table for the rows, divide each number in each row by the total in
that row.
|Topping |Sprinkles |m & m’s |Nothing |Total |
|Chocolate | | | | |
3) To create a relative-frequency two way table for the columns, divide each number in each column by the
total in that column.
|Topping |Sprinkles |m & m’s |Nothing |
|Vanilla | | | |
|Chocolate | | | |
|Total | | | |
4) To create a relative-frequency two way table with percents, use the total number of students.
|Topping |Sprinkles |m & m’s |Nothing |Total |
|Chocolate | | | | |
|Total | | | | |
Lesson 11 – Two-Way Frequency Table (Bivariate data) Classwork Day 11
5) Jeremy asked a sample of 40 8th grade students whether or not they had a curfew. He then asked if they had
a set bedtime for school nights. He recorded his data in this two-way frequency table.
Create a two-way relative frequency table for these data.
| |Bedtime |No Bedtime |Total |
|Curfew |21 |4 |25 |
|No Curfew |3 |12 |15 |
|Total |24 |16 |40 |
| |Bedtime |No Bedtime |Total |
|Curfew | | | |
|No Curfew | | | |
6) The table shows the grade levels and primary home languages for all the students at Martin Middle School.
| |6th Grade |7th Grade |8th Grade |Total |
|English |104 |99 |116 |319 |
|Other |56 |81 |84 |221 |
|Total |160 |180 |200 |540 |
Use the grid below to create a two-way relative frequency table.
| |6th Grade |7th Grade |8th Grade |
|English | | | |
|Other | | | |
|Total | | | |
7) A recent poll asked whether customers like a restaurant’s new lunch menu. Complete the corresponding
relative frequency table with respect to the total population.
Frequency Table Total Relative Frequency Table
New Menu New Menu
| |Yes |No |Total |
|Male |13 |15 |28 |
|Female |18 |25 |43 |
|Total |31 |40 |71 |
| |Yes |No |Total |
|Male | | | |
|Female | | | |
|Total | | | |
8) Lucia asked 50 eighth-grade students if they agreed or disagreed with a proposed plan to start the school
day at a later time. She also recorded whether each student responding was a boy or girl. Make several
observations about the data. Create a two-way relative frequency table for these data:
| |Boys |Girls |Total |
|Agree |14 |12 |26 |
|Disagree |6 |18 |24 |
|Total |20 |30 |50 |
Lesson 11 – Two-Way Frequency Table (Bivariate data) Classwork Day 11
9) Circle the table that will be more helpful in finding whether male or female teenagers are more likely to
own a car.
Frequency Table Total Relative Frequency Table
Car Ownership Car Ownership
| |Yes |No |Total |
|Male |49 |126 |175 |
|Female |48 |102 |150 |
|Total |97 |228 |325 |
| |Yes |No |Total |
|Male |28% |72% |100% |
|Female |32% |68% |100% |
|Total |29.8% |70.2% |100% |
Justify your answer: ____________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
10) Fifty moviegoers were surveyed about their favorite movie types.
• 13 men and 6 women chose “Action”as their favorite type.
• 8 men and 8 women chose “Drama”as their favorite type.
• 5 men and 4 women chose “Comedy”as their favorite type.
• 4 men and 2 women chose “Animated”as their favorite type.
Draw a two-way frequency table using the above data. Use the table to determine the most popular type of movie in the survey.
| |Action |Drama |Comedy |Animated |Total |
|Women | | | | | |
|Total | | | | | |
Which type of movie surveyed is most popular? __________________
11) The frequency table shows the hair and eye color of 25 students. Is there evidence that blue eyes are more common for students with blond hair than those with black hair?
Write a valid conclusion. ____________________________________________________________________
_________________________________________________________________________________________
| |Blond |Black |Brown |Total |
|Blue |3 |1 |2 |6 |
|Brown |2 |7 |6 |15 |
|Green |1 |1 |2 |4 |
|Total |6 |9 |10 |25 |
Two-Way Frequency Table (Bivariate data) Lesson 11 – Homework
1) Complete the table.
| |Football |Baseball |Total |
|Coaches |5 |7 |12 |
|Players | |6 | |
|Total |12 | | |
a) How many coaches participated in the survey?
b) How many players participated in the survey?
c) Which sport is more popular among the coaches?
d) Which sport is more popular among the players?
2) Twenty students were surveyed about their favorite subject. Below are the results.
• 3 boys and 4 girls chose Math
• 2 boys and 3 girls chose Science
• 1 boys and 2 girls chose ELA
• 3 boys and 2 girls chose History
Construct a two-way frequency table for the data.
| |Math |Science |ELA |History |Total |
|Girls | | | | | |
|Total | | | | | |
According to the table, what is the least popular subject? _____________
a) Construct a two way relative frequency table based on percent
| |Math |Science |ELA |History |
|Boys | | | | |
|Girls | | | | |
|Total | | | | |
3) The two- way shows the results of a survey about whether students should be required to wear school
uniforms. According to the table, what percent of teenagers are in favor of wearing school uniforms?
| |For |Against |Total |
|Parents |0.42 |0.07 |0.50 |
|Teens |0.18 |0.32 |0.50 |
|Total |0.61 |0.39 |1.00 |
a) If 300 parents were surveyed, how many were for wearing uniforms?
-----------------------
Unit 9
[pic]
7th Accelerated
Name:___________________________
Teacher:_________________________
Period:________
Food and Yard Waste
11%
Plastic
24%
Paper
30%
Other Trash
35%
[pic]
[pic]
[pic]
40%
Move the decimal point one place to the left.
10% of 50 is ___!
Example: 10% of 50
10% of 50
If 10% of 60 is 6,
then 5% of 60 is ___!
Example:
5% of 60
Method 2:
The price of the item is 100%
AND tax is 8%
100% + 8% = 108%
So,
108% • $459 = $495.72
This is the grand total
(including tax)
[pic]
Sydney
Percent of change =
= 0.08 = 8%
Jared
Percent of change =
= 0.087 = 8.7%
Percent Error Formula:
[pic]
Relative Error Formula:
[pic][pic]
Relative Error Formula:
[pic][pic]
Percent Error Formula:
[pic]
I = (p)(r)(t)
| |Boys |Girls |Total |
|Agree | | |100% |
|Disagree | | |100% |
| |Blond |Black |Brown |Total |
|Blue | | | | |
|Brown | | | | |
|Green | | | | |
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