Ch - Laurel County
7.RP.1
Selected Response
SELECT THE CORRECT ANSWER.
1. A carpenter lays 16 square feet of tile in [pic] of an hour. How many square feet of tile does the carpenter lay per hour?
[pic] 24 square feet per hour
[pic] [pic] square feet per hour
[pic] [pic] square feet per hour
[pic] [pic] square foot per hour
2. Determine the unit rate of a marathon runner who travels [pic] miles in [pic] hour.
[pic] 10 mi/h [pic] [pic] mi/h
[pic] [pic] mi/h [pic] [pic] mi/h
3. One-quarter of a bread recipe calls for
[pic] cup of bread flour. How many cups are needed per recipe?
[pic] [pic] cup [pic] [pic] cup
[pic] [pic] cup [pic] [pic] cups
4. A shoreline is eroding at a rate of [pic] foot per 3 months. How many feet are eroding per year?
[pic] [pic] foot per year
[pic] [pic] foot per year
[pic] [pic] feet per year
[pic] 9 feet per year
Select all correct answers.
5. A car rental agency initially offers a car that can go 304 miles on [pic] gallons of gasoline. There are other vehicles available at the agency, shown below. Which of the other cars have a greater unit rate of miles per gallon than the recommended car?
[pic] 187 miles on [pic] gallons
[pic] 357 miles on [pic] gallons
[pic] 216 miles on [pic] gallons
[pic] 209 miles on [pic] gallons
[pic] 115 miles on [pic] gallons
Match each unit rate with the corresponding situation.
| 6. [pic] miles per hour | A [pic] mile in [pic] hour |
|7. [pic] miles per hour |B [pic] mile in [pic] hour |
|8. [pic] miles per hour |C [pic] miles in [pic] hour |
|9. [pic] miles per hour |D [pic] mile in [pic] hour |
Constructed Response
10. DEREK APPLIES GRASS SEED TO [pic] ACRE IN
[pic] HOUR. HOW MANY ACRES CAN DEREK COVER PER HOUR?
11. A convenience store sells [pic] pound of one brand of trail mix for $1.50 and
[pic] pound of another brand of trail mix for $2.15. Which brand has a lower price per pound? Explain your reasoning.
12. Two buckets filled with a liquid are leaking. The first bucket leaks at a rate of [pic] gallon per [pic] hour. The second bucket leaks at a rate of [pic] gallon per [pic] hour. Which container leaks water less rapidly? Explain your reasoning.
13. Laura decides to walk to her job. She walks [pic] miles in [pic] hour.
a. What is Laura’s walking rate?
b. Laura’s job is [pic] miles away. If she starts walking to her job at 9:00 a.m. and is scheduled to start working at 11:00 a.m., will she arrive at her job on time? Explain your reasoning.
14. An experiment measured the evaporation rates of two liquids, liquid A and liquid B, at a certain temperature and pressure. After [pic] hour, [pic] cup of liquid A evaporated. After [pic] hour, [pic] cup of liquid B evaporated.
a. What is the unit rate for the evaporation of liquid A?
b. What is the unit rate for the evaporation of liquid B?
c. Which liquid evaporated faster and by how much?
15. Two leaky containers are filling with water. Water enters container A at a rate of [pic] cup per [pic] minute and leaks out at a rate of [pic] cup per [pic] minute. Water enters container B at a rate of [pic] cup per [pic] minute and leaks out at a rate of
[pic] cup per [pic] minute. Which container needs to be filled faster in order for both containers to gain the same amount of water per minute? By how much more water per minute? Explain.
7.RP.2a
Selected Response
SELECT THE CORRECT ANSWER.
1. Tell whether the relationship is a proportional relationship. Explain why or why not.
[pic]
[pic] The relationship is proportional because a single line can be drawn through all the points and the line passes through the origin.
[pic] The relationship is proportional because a single line can be drawn through all the points.
[pic] The relationship is not proportional because a single line can be drawn through the points but it does not pass through the origin.
[pic] The relationship is not proportional because a single line cannot be drawn through all the points.
2. Tell whether the relationship is a proportional relationship. Explain why or why not.
|Hours | Dollars Earned |
| 4 | 50.00 |
| 5 | 62.50 |
| 6 | 75.00 |
| 7 | 87.50 |
| 8 | 100.00 |
[pic] The relationship is proportional because the ratio of dollars earned to the number of hours is 12.50.
[pic] The relationship is proportional because the ratio of dollars earned to the number of hours is 50.
[pic] The relationship is proportional because the ratio of dollars earned to the number of hours is 100.
[pic] The relationship is not proportional because the ratio of dollars earned to the number of hours is not constant.
Select all correct answers.
3. Which of the following situations form a proportional relationship with milk that costs $3.29 per gallon?
[pic] 3 gallons of milk for $6.57
[pic] 4 gallons of milk for $13.16
[pic] 5 gallons of milk for $16.45
[pic] 9 gallons of milk for $29.61
[pic] 12 gallons of milk for $40.68
4. Which of the following situations form a proportional relationship?
[pic] 5 DVDs for $9 and 15 DVDs for $27
[pic] 6 cups of coffee for $8 and 9 cups of coffee for $12
[pic] 3 pocketbooks for $60 and
5 pocketbooks for $90
[pic] 12 cans for $3 and 30 cans for $7.50
[pic] 2 ink cartridges for $25 and 4 ink cartridges for $75
CONSTRUCTED RESPONSE
5. A TIMER IS STARTED AS A BALL IS DROPPED FROM A CERTAIN HEIGHT AND ITS VELOCITY MEASURED. AFTER 0 SECONDS, THE BALL IS FALLING AT 0 FEET PER SECOND. AFTER
2 SECONDS, THE BALL IS FALLING AT 64 FEET PER SECOND. AFTER 3 SECONDS, THE BALL IS TRAVELING AT 144 FEET PER SECOND. IS THIS A PROPORTIONAL RELATIONSHIP? EXPLAIN WHY OR WHY NOT.
6. What value completes the table to make the relationship between the two quantities proportional? Explain your reasoning.
|Items |Weight (oz) |
|7 |31.5 |
|9 |40.5 |
|10 | ? |
|12 |54 |
|15 |67.5 |
7. The table shows the distance a cheetah travels. Tell whether the relationship is a proportional relationship. If so, tell how far the cheetah travels in 14 seconds.
|Time (seconds) |Distance (feet) |
| 2 | 134 |
| 3 | 201 |
| 4 | 268 |
| 5 | 335 |
| 6 | 402 |
8. a. A video game rental store was charging $6 per rental. Complete the table below.
|Video games |Cost ($) |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
b. The store now charges a $5 one-time fee and then $4 per rental. Complete the table below.
|Video games |Cost ($) |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
c. Graph the points from the first table on the coordinate plane and draw a line through them. Repeat this process for the points in the second table.
[pic]
d. Use the graphs to describe whether each table of values represents a proportional relationship. Explain.
7.RP.2b
SELECTED RESPONSE
SELECT THE CORRECT ANSWER.
1. Tell whether the relationship is a proportional relationship. If so, give the constant of proportionality.
[pic]
[pic] The relationship is proportional. The constant of proportionality is 2.5.
[pic] The relationship is proportional. The constant of proportionality is 5.
[pic] The relationship is proportional. The constant of proportionality is 20.
[pic] The relationship is not proportional.
2. Find the missing value for the proportional relationship, in which the number of cents depends on the number of minutes.
|Minutes |Cents |
|3 |60 |
|7 |140 |
|13 | |
|16 |320 |
|23 |460 |
[pic] [pic]
[pic] 20
[pic] 220
[pic] 260
3. Three tubes of brand A toothpaste cost $12, five tubes of brand B toothpaste cost $25, and eight tubes of brand C toothpaste cost $32. Is the relationship between the number of tubes of toothpaste and the cost a proportional relationship? If it is, give the constant of proportionality assuming that cost depends on the number of tubes bought.
[pic] The relationship is proportional.
The constant of proportionality is
$4 per tube.
[pic] The relationship is proportional.
The constant of proportionality is
$5 per tube.
[pic] The relationship is proportional.
The constant of proportionality is
$12 per tube.
[pic] The relationship is not proportional.
Select all correct answers.
4. A grocery store offers 4 cans of store-brand vegetables for $3.00. On nearby shelves, other brands are available at the prices shown below. Which of the offers have a unit rate that is less than the store-brand unit rate?
[pic] 2 cans for $1.25
[pic] 3 cans for $2.00
[pic] 4 cans for $3.20
[pic] 5 cans for $3.60
[pic] 10 cans for $7.50
Select the correct answer for each
lettered part.
5. The points (3, 8) and (9, 24) are on the graph of a proportional relationship. Determine whether each point belongs on the same graph.
a. (0, 0) [pic] Yes [pic] No
b. (1, 3) [pic] Yes [pic] No
c. (6, 16) [pic] Yes [pic] No
d. (12, 32) [pic] Yes [pic] No
e. (27, 192) [pic] Yes [pic] No
CONSTRUCTED RESPONSE
6. THE AMOUNT ANTWAN EARNS MOWING LAWNS DEPENDS ON THE NUMBER OF HOURS HE WORKS, AND THE RELATIONSHIP IS PROPORTIONAL. ANTWAN EARNS $69.00 FOR WORKING 6 HOURS. COMPLETE THE TABLE. THEN GIVE THE VALUE OF THE CONSTANT OF PROPORTIONALITY, AND EXPLAIN ITS MEANING IN THIS SITUATION.
|Time |Earnings |
|(hours) |(dollars) |
|3 | |
| |57.50 |
|8 | |
| |97.75 |
|11 | |
| |138.00 |
7. Angela wrote the data values in the table shown below and claimed that it shows a proportional relationship.
|x |y |
|10 |16.0 |
|14 |28.0 |
|18 |28.8 |
a. Explain why Angela’s claim is not correct.
b. There are two ways to change exactly one cell in the table so that the table will show a proportional relationship. Find both ways to do this. Explain your reasoning.
8. The ratio of the number of players to the number of soccer teams is constant. Complete the table using this ratio.
|Teams |Players |
|3 | |
|4 | |
|5 |70 |
|6 | |
|8 | |
9. The table shows prices that three people paid for the same kind of fresh salmon at Fiona’s Fish Factory.
|Weight, w |Price, p |
|3 lb. |$29.25 |
|5 lb. |$48.75 |
|8 lb. |$78.00 |
a. Explain why this is a proportional relationship.
b. The equation p ’ kw shows the relationship between price p and weight w. What is the value of the constant of proportionality k in this situation? What is the meaning of the constant of proportionality?
c. Fiona’s Fish Factory decides to give $10 off to everyone who buys
2 pounds of salmon or more. Make a table showing the prices for buying 3, 5, and 8 pounds of salmon now. Is the relationship still proportional? Explain why or why not.
7.RP.2c
SELECTED RESPONSE
SELECT THE CORRECT ANSWER.
1. The graph shows how the number of people p seated at an event is related to the number of tables t provided. Tell whether the quantities are in a proportional relationship. If so, write an equation that represents the relationship.
[pic]
[pic] proportional; [pic]
[pic] proportional; p ’ 3t
[pic] proportional; p ’ 12t
[pic] The quantities are not in a proportional relationship.
2. Renting a canoe costs $5.00 per hour for each adult and $2.50 per hour for each child. One adult and two children decide to rent a canoe. What is an equation that shows the relationship between cost c in dollars and time t in hours?
[pic] c ’ 5.00t + 2.50
[pic] c ’ 5.00 + 2.50t
[pic] c ’ 7.50t
[pic] c ’ 10.00t
3. The cost of ham c depends on the weight w bought. Tell whether the quantities are in a proportional relationship. If so, write an equation that represents the relationship.
|Weight, w |Cost, c |
|(pounds) |(dollars) |
|2 |13.00 |
|3 |19.50 |
|4 |26.00 |
|5 |32.50 |
[pic] This relationship is proportional. The equation is c ’ [pic]w.
[pic] This relationship is proportional. The equation is c ’ 6.5w.
[pic] This relationship is proportional. The equation is c ’ 13w.
[pic] This relationship is not proportional.
Select all correct answers.
4. Which of the following equations represent a proportional relationship?
[pic] y ’ 2x + 2 [pic] y ’[pic]
[pic] y ’ [pic] [pic] y ’ 80x
[pic] y ’ 5 [pic] y ’ 4 − x
CONSTRUCTED RESPONSE
5. A CAR WITH A DIESEL ENGINE TRAVELS
663 MILES USING 13 GALLONS OF FUEL. SUPPOSE THAT THE RELATIONSHIP BETWEEN THE DISTANCE TRAVELED AND THE AMOUNT OF FUEL USED BY THIS CAR IS PROPORTIONAL. WRITE AN EQUATION TO REPRESENT THIS RELATIONSHIP. DEFINE ANY VARIABLES YOU USE.
6. Marsha is selling frozen yogurt at a town concert to help raise money for the local library. The earnings for the library y are proportional to the number of frozen yogurts x she sells.
a. Complete the table below.
|Frozen yogurts |Earnings |
| |(dollars) |
|2 | |
| |14 |
|6 |21 |
| |28 |
|10 | |
b. What is an equation for the relationship?
c. Plot the points from part a and draw the line of the equation from part b onto the graph below.
[pic]
d. If Marsha wants to raise $245 for the library, how many frozen yogurts would she have to sell? Explain how you found your answer.
7. A farmer’s market is selling three different cheeses. The sign for cheddar states, “The cost is only $6.25 per pound!”
The sign for mozzarella has the
following table.
|Weight |Cost |
|(pounds) |(dollars) |
|2 |11.00 |
|3 |16.50 |
|4 |22.00 |
|5 |27.50 |
The sign for provolone, written by a former algebra teacher, states, “The cost y for x pounds is given by y ’ 5.75x.”
a. Find the equation that gives the cost y of buying x pounds of cheddar. Explain.
b. Find the equation that gives the cost y of buying x pounds of mozzarella. Explain.
c. Order the cheeses from least to most expensive. Explain your answer.
7.RP.2d
SELECTED RESPONSE
SELECT THE CORRECT ANSWER.
1. The ordered pairs show equal amounts of money in U.S. dollars and euros.
[pic]
What other ordered pair on this graph would show the unit rate? What does the ordered pair represent in this situation?
[pic] (1, 0.78); 0.78 dollar equals 1 euro.
[pic] (1, 0.78); 0.78 euro equals 1 dollar.
[pic] (1, 1.28); 1.28 dollars equals 1 euro.
[pic] (1, 78); 78 euros equals 1 dollar.
2. The graph below shows the relationship between the time in hours and the area mowed in acres. What point means mowing 8 acres in 5 hours?
[pic]
[pic] (0, 0) [pic] (5, 8)
[pic] (1, 1.6) [pic] (8, 5)
3. The graph below shows the relationship between the number of dogs and the number of cats. What does the point
(9, 36) represent?
[pic]
[pic] There are 9 dogs when there are
9 cats.
[pic] There are 36 cats when there are
9 dogs.
[pic] There are 36 dogs when there are
9 cats.
[pic] There are 36 dogs when there are
36 cats.
Select all correct answers.
4. Each of the following points is on a graph of a proportional relationship. Which of the following points are on a line with a unit rate that is less than 1?
[pic] (1, 2)
[pic] (1, 1)
[pic] (1, 0.5)
[pic] (1, 20)
[pic] (1, 0.1)
CONSTRUCTED RESPONSE
5. THE GRAPH BELOW SHOWS THE RELATIONSHIP BETWEEN THE NUMBER OF THEATER TICKETS BOUGHT AND THE COST. WHAT IS THE ORDERED PAIR THAT HAS AN X-COORDINATE OF 1? WHAT IS THE MEANING OF THAT ORDERED PAIR?
[pic]
6. Kim is running in a race. The number of miles she runs and the number of minutes it takes to run them are in a proportional relationship. Determine an equation that reasonably represents this relationship and draw the line onto the graph below. Plot the points where
x ’ 0, x ’ 1, and a third point on the
line. Then describe what the three
points mean.
[pic]
7. The graph below shows the proportional relationship between the number of square yards of fabric and the cost in dollars. Does the line going through the point (0, 0) make sense? Explain your reasoning.
[pic]
8. Think of a reasonable proportional relationship whose graph contains the point (2, 120). Provide the appropriate labels for the axes of the graph below.
[pic]
Explain what the ordered pairs (2, 120) and (0, 0) mean in the situation you provided. Then find the ordered pair on the line that has an x-coordinate of 1 and explain what that ordered pair means in your situation.
7.RP.3
SELECTED RESPONSE
SELECT THE CORRECT ANSWER.
1. The tip for excellent service in a restaurant is $20 for every $100 of the meal. What is the total bill (cost of meal plus tip) for a $60 meal?
[pic] $12.00
[pic] $48.00
[pic] $72.00
[pic] $120.00
2. A department store has a discount on shoes based on a percentage of the price. Suppose one pair of shoes is marked down from $70 to $49. What is the price for a $110 pair of shoes after the discount is applied?
[pic] $89.00
[pic] $77.00
[pic] $73.33
[pic] $33.00
3. The number of fans who attended a softball game increased from 1,200 for the first game to 1,500 for the second game. How many fans will attend the third game if the same percent
increase occurs?
[pic] 375
[pic] 1,800
[pic] 1,875
[pic] 2,700
4. Isabella earns simple interest on her savings account. She deposits $1,200 into her account and will have $1,344 after 2 years. How much will Isabella have in her account 7 years after her initial deposit?
[pic] $1,704
[pic] $1,848
[pic] $2,208
[pic] $4,704
Select all correct answers.
5. Each of the following bills is late. Which of the following situations charges a fee that is greater than 5%?
[pic] A $150 bill totals $154.50 with fee.
[pic] A $40 bill totals $41.60 with fee.
[pic] A $120 bill totals $132.00 with fee.
[pic] A $220 bill totals $237.60 with fee.
[pic] A $410 bill totals $418.20 with fee.
Match the situation with the percent
of discount.
| 6. A $55.00 purse is on sale for $30.25. | A 20% |
|7. A $98.00 power inverter is on sale for $78.40.|B 25% |
|8. A $44.00 video game |C 30% |
|is on sale for $28.60. |D 35% |
|9. A $37.50 dress is on sale for $26.25. |E 40% |
| |F 45% |
CONSTRUCTED RESPONSE
10. THE SALES COMMISSION IS 10% AT AN ELECTRONICS STORE. HOW MUCH DOES SAUL HAVE TO SELL IN 22 HOURS TO EARN $12.50 PER HOUR FROM COMMISSION? EXPLAIN.
11. A $45.00 purchase in Iowa totals $47.70 with tax and a $35.00 purchase in Tennessee totals $37.45 with tax. Which state has a greater sales tax percentage? Explain your reasoning.
12. Amanda measures the top of an 80 cm desk to be 82.4 cm. Dwayne measures the height of a 140 cm cabinet to be 137.2 cm. Which student has a greater percent error? Explain your reasoning.
13. Chelsea deposits $600.00 into a bank account and is earning simple interest from the bank. After 4 years, her account has a balance of $621.60. If Chelsea decided to put $1,100.00 into the account instead of $600.00, how much would she have after 7 years? Explain.
14. Carlos’s family had breakfast at one restaurant and dinner at another restaurant while on vacation. The service during breakfast was terrible and the cost for the meal was $44.50. Carlos’s total bill (cost of meal and tip) was $49.84. The service during dinner was excellent and the cost for the meal was $57.50.
a. What was the percentage of the tip for breakfast?
b. Carlos decided the tip’s percentage for dinner should be 50% more than the tip’s percentage for breakfast. What percent did Carlos give for a tip during dinner?
c. What was the amount of the tip and the total bill (cost of meal and tip) for dinner using the percentage of the tip from part b?
15. Ray owns property that had a value last year of $164,000. Ray paid $3,280 in property tax to his city last year.
a. Find the property tax rate last year.
b. The city increases its property tax rate by 10% of last year’s rate. Find this year’s property tax rate.
c. Ray’s property value decreased after an assessment this year to $135,000. Find Ray’s property tax this year.
d. How is it possible that Ray’s property tax is less this year even though the property tax rate increased?
16. Jasmine owns a jewelry store and marks up the price from the distributor to earn a profit. She buys a necklace for $100, a pair of earrings for $130, and a ring for $160. She wants to earn at least $40 on each of the items but does not want to mark up any price by more than $80.
a. What is the range of percents that Jasmine can mark up each item so that it fits into her criteria?
b. Suppose Jasmine wants to mark up all 3 items using the same percent but also maximize her profit. What percent should she use?
c. Using the percent from part b, find each marked up price.
d. Using the results from part c, find her total profit.
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