Real World Systems Booklet Project.docx



The Real Life Systems BookletProject Given: 2/26/201510 Extra Points if Project is turned in on: 3/11/2015Select six problems from the word problems given to demonstrate your knowledge of how to apply systems of linear equations to solve problems. You cannot choose more than one problem from each category. As indicated before each set of problems, the categories are as follows: 1) Ticket Problems, 2) Total Quantity and Total Dollar Amount Problems, 3) Vehicle/Passengers Problems, 4) Linear Programming Problems, 5) Age Problems, and 6) Miscellaneous. Your booklet will contain 3 main sections. Cover Page (10 points)Table of Contents (10 points)Coin and Dollar Bill Problem……………………………………………………………..2Vehicle/Passengers Problem..…………………………………………………………..3Six Problem Pages (72 points)Last 8 points comes from turning project in on time.Place the name of the category in which the problem belongs at the top of the section. Use pictures to illustrate the problem. Your work should be neat. **Suggestion: Manually write your steps, work out each problem on a separate piece of paper. Once you know your work is correct transfer neatly to your final produce.Cover Page should contain the following information:Title3 pointsName3 pointsDate1 pointSubject1 pointTeacher Name1 pointBlock1 pointNo Color or Creativity- 5 pointsChoose a theme for your project. Once you choose a theme change underlined pronouns to fit characters or places that fit your theme.ExamplesThemeSuperhero TeamFootball TeamTV ShowNameName of Superhero or VillianName of Football Players or MascotName of Characters on the ShowPlaceName of Superhero’s hideoutName of Football team’s arenaName of city Show is based inYour theme should be clearly represented throughout booklet. Understand you can lose up to 20 points if theme is not clearly represented by words and/or pictures throughout booklet.The Real Life Systems BookletCover Page Points:Table of Contents Points:Ticket ProblemsPossible PointsPoints EarnedName of Category Present +1Let Statements Present+2Two Equation Written+2Clear and Detailed Work+5Correct Answer Present+2DeductionsPage is NOT neat-4Did not rewrite problem on page-2Picture/Color Missing-2Final Answer is NOT written in a complete sentence-2Total Page Points:Total Quantity and Total Dollar Bill Problem Possible PointsPoints EarnedName of Category Present +1Let Statements Present+2Two Equation Written+2Clear and Detailed Work+5Correct Answer Present+2DeductionsPage is NOT neat-4Did not rewrite problem on page-2Picture/Color Missing-2Final Answer is NOT written in a complete sentence-2Total Page Points:Vehicle/Passengers ProblemPossible PointsPoints EarnedName of Category Present +1Let Statements Present+2Two Equation Written+2Clear and Detailed Work+5Correct Answer Present+2DeductionsPage is NOT neat-4Did not rewrite problem on page-2Picture/Color Missing-2Final Answer is NOT written in a complete sentence-2Total Page Points:Linear Programming ProblemPossible PointsPoints EarnedName of Category Present +1LP Table Set-Up+2Inequalities Graphed+2Clear and Detailed Work+5Correct Answer Present+2DeductionsPage is NOT neat-4Did not rewrite problem on page-2Picture/Color Missing-2Final Answer is NOT written in a complete sentence-2Total Page Points:Age ProblemPossible PointsPoints EarnedName of Category Present +1Let Statements Present+2Two Equation Written+2Clear and Detailed Work+5Correct Answer Present+2DeductionsPage is NOT neat-4Did not rewrite problem on page-2Picture/Color Missing-2Final Answer is NOT written in a complete sentence-2Total Page Points:Miscellaneous ProblemPossible PointsPoints EarnedName of Category Present +1Let Statements Present+2Two Equation Written+2Clear and Detailed Work+5Correct Answer Present+2DeductionsPage is NOT neat-4Did not rewrite problem on page-2Picture/Color Missing-2Final Answer is NOT written in a complete sentence-2Total Page Points:On Time (+ 8 points)-1777990Grade _____________Real Life Systems of Linear Equations ProjectSystems of Linear Equations Application ProblemsTicket Problems353 people attend a local play at a private club. Members get tickets for $2.75, while non-members have to pay $6.00. If the total gate for the play came to $1793, how many members and non-members came to the play?58 people attend a banquet at Disney. Residents paid $13.00 and non-residents paid $17.50. If Disney made $925.00 from ticket sales for the event, how many residents and non-residents attended?At Carowinds, adult tickets cost $22 and tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. Write and solve a system of equations to find how many children and how many adults were in the group.The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.From the local YMCA, 105 adults and and kids will attend the local fair. Advanced adult tickets for the fair will cost $8 and and advanced kid tickets will cost $5. The organization received a bill for $645. How many adult tickets were purchasedBrenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?Total Quantity and Total Dollar AmountAt an ice cream parlor, ice cream cost $1.10 and sundaes cost $2.35. One day, the receipts for a total of 172 cones and sundaes were $294.20. How many cones were sold? Jim runs a food cart and during a busy outdoor festival he sold $8470 worth of food. He sells hot dogs for $2.50 and steak sandwiches for $10.00. If he sold a total of 985 items that day, how many of each item did he sell?Brandon has a collection of 25 pair of Jordans and Adidas shoes. The average cost for the Jordans are $165, while the average cost of the Adidas are $80. The value of the collection is $2850. How many pair of Jordans are in the collection.Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 shirts then how many of each kind did she buy?Tyler is catering a banquet for 250 people. Each person will be served either a chicken dish that costs $5 each or a beef dish that costs $7 each. Tyler spent $1500. How many dishes of each type did Tyler serve? Vehicle/Passengers ProblemsMr. LS and Ms. AJ are going to reward the students in the school by taking them to 6 Flags in Georgia. Mr. LS will rent 8 vans and 8 buses to transport 240 kids while Ms. AJ will fill 4 vans and 1 bus for the remaining 54 students. Each bus and each van will carry the same number of students. How many students will ride on each van? How many students will ride on each bus?Mr. JB and Ms. BH will be taking another group of students on a separate trip to Myrtle Beach. Mr. JB will fill 1 van and 6 buses with 372 students while Ms. BH will rent 4 vans and 12 buses for 780 students. Each van and each bus will carry the same number of students. How many students will ride in each van? How many students will ride on each bus?Mr. DD and Ms. IP decided to take the remaining students to a local park. Mr. DD will fill 4 SUV’s and 5 cars for 102 students. Ms. IP will need load 7 SUV’s and 5 cars for 126 students. Each SUV and car will carry the same number of students. How many students will ride in each SUV? How many students will ride in each car?A school is planning a field trip to Washington Monument for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. Write and solve a system of equations to find how many buses and how many vans will be needed.A class of 195 students went on a field trip to New York City. They took 7 vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds 5 students and each bus holds 45 students.All 231 students in the Math Club went on a field trip Discovery Place. Some students rode in vans which holds 7 students each and some students rode in buses which hold 25 students each. How many of each type of vehicle did they use if there 15 vehicles total?Linear Programming ProblemsVariablesConstraintsTotalsConstraint 1:Constraint 2:Maximizing(Do Not Graph)PFarmer Jim can plant up to 8 acres of land with wheat and barley. He can earn $5,000 for every acre he plants with wheat and $3,000 for every acre he plants with barley. Farmer Jim use of a necessary pesticide is limited by federal regulations to 10 gallons for his entire 8 acres. Wheat requires 2 gallons of pesticide for every acre planted and barley requires just 1 gallon per acre. What is the maximum profit he can make?Mary works a part-time job, selling cards over the telephone. She sells two types of cards, birthday cards and holiday cards. Mary makes $2.00 for each box of birthday cards she sells, and she makes $2.50 for each box of holiday cards she sells. Mary can work no more than 10 hours (600 minutes) per week. It takes her an average of 15 minutes to sell one box of birthday cards and an average of 20 minutes to sell one box of holiday cards. If Mary can sell no more than 35 boxes of cards in total, how many boxes of each type should she sell to make the most money?Fred's Coffee sells two blends of beans: Yusip Blend and Exotic Blend. Yusip Blend is one-half Costa Rican beans and one-half Ethiopian beans. Exotic Blend is one-quarter Costa Rican beans and three-quarters Ethiopian beans. Profit on the Yusip Blend is $3.50 per pound, while profit on the Exotic Blend is $4.00 per pound. Each day Fred receives a shipment of 200 pounds of Costa Rican beans and 330 pounds of Ethiopian beans to use for the two blends. How many pounds of each blend should be prepared each day to maximize profit? What is the maximum profit?A manufacturer of ski clothing makes ski pants and ski jackets. The profit on a pair of ski pants is $2.00 and on a jacket is $1.50. Both pants and jackets require the work of sewing operators and cutters. There are 60 minutes of sewing operator time and 48 minutes of cutter time available. It takes 8 minutes to sew one pair of ski pants and 4 minutes to sew one jacket. Cutters take 4 minutes on pants and 8 minutes on a jacket. Find the maximum profit and the amount of pants and jackets to maximize profit.Food and clothing are shipped to survivors of a natural disaster.? Each carton of food will feed 12 people, while each carton of clothing will help 5 people.? Each 20-cubic-foot box of food weighs 50 pounds and each 10-cubic-foot box of clothing weighs 20 pounds.? The commercial carriers transporting food and clothing are bound by the following constraints:The total weight cannot exceed 19,000 pounds.The total volume must be no more than 8000 cubic feet.How many cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped?Jim is given a test where computation problems are worth 6 points and word problems are worth 10 points.? It takes Jim 2 minutes to solve a computation problem and 4 minutes to solve a word problem.? Jim only has 40 minutes to take the test and can answer no more than 12 problems.? How many of each problem should Jim answer to get the most points?Age ProblemsIf twice the Billy’s age in years is added to the Hunter’s age, the sum is 70. But if twice the Hunter’s age is added to the Billy's age, the sum is 95. Find the ages of Hunter and Billy.Tom’s age minus Bob’s age is 2. Bob’s age is 82 less than three times Tom’s age. How old is Tom and Bob?Sandy is 15 years older than Karen. The sum of Sandy’s age and Karen’s age is 69. How old is Sandy and Karen?The sum of Ava and Jordan’s age is 20. Jordan is 4 years older than Ava. How old is Ava and Jordan?Carly is 4 times Darryl’s age. The sum of their ages is equal to 45. How old is Carly and Darryl?Emma is 2 times Ben’s age minus 16. Ben is equal to the sum of Emma’s age and 3. How old is Ben and Emma?Miscellaneous Bob ate 10 carrots and 7 Hershey’s kisses and the total calories were 263. Fred ate 4 carrots and 8 Hershey’s kisses and the total calories were 230. How many calories are in a carrot and a Hershey’s kiss?Dina bought supplies for a party. Three rolls of streamers and 15 party hats cost $30. Later, Dina bought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers cost? How much did each party hat cost?Tony Purchases 8 gallons of paint and 3 brushes for $152.50. The next day, Tony purchases 6 gallons of paint and 2 brushes for $113.00. How much does each gallon of paint and each brush cost?At McDonald’s four cheeseburgers and three medium fries have a total of 2290 calories. Six cheeseburgers and two medium fries have 2560 calories. How many calories does each item contain?A Ralph’s farmhouse shelters 11 animals. Some are goats and some are ducks. Altogether there are 34 legs. How many of each animal are there?Brodie’s Gourmet Pretzel Shop specializes in selling the very finest chocolate covered pretzels. Banky bought 4 white chocolate pretzels and 6 dark chocolate pretzels for $10.50. Holden bought 8 white chocolate and 3 dark chocolate pretzels for $9.75. ................
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