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Real Life Systems of Linear Equations Project Students will understand systems of linear equations and use them to solve problems. a. Given a problem in context, write an appropriate system of linear equations. b. Solve systems of equations graphically and algebraically, using technology as appropriate. c. Interpret solutions in problems context. Select one problem from each section to demonstrate your knowledge of how to apply systems of linear equations to solve problems. You can not choose more than one problem from each category. For each problem, use a new piece of paper divided into three sections. 1. Paste the actual problem on the paper in the section in which you will show how to work out the problem. 2. Place the name of the category in which the problem belongs at the top of the section (Graphing, Substitution, Elimination). 3. Write a Systems of Equation to model the given situation. 4. Solve the Systems of Equations. 5. Write a sentence to explain what the solution represents in terms of the problem. 6. Use pictures to illustrate the problem. 7. Your work should be neat. Therefore, you should work out each problem on a separate piece of paper before transferring your answer to the final copy. Create a written response for the following questions in complete sentences: 1. Which method did you find the easiest to complete? Why? 2. Which method did you find the hardest to complete? Why? Real Life Systems of Linear Equations Project DUE: ___________________________________ Graphing Substitution Equations (2) _____________ Equations (2) _____________ Solution (1) _____________ Solution (1) _____________ Sentence (1) _____________ Sentence (1) _____________ Picture (1) _____________ Picture (1) _____________ Elimination Written Response Equations (2) _____________ Question 1 response (1) _____________ Solution (1) _____________ Question 2 response (1) _____________ Sentence (1) _____________ Complete Sentences (2) _____________ Picture (1) _____________ Overall Neatness of Project (2) ________ Grade ____________ out of 21 points Real Life Systems of Linear Equations Project GRAPHING SUBSTITUTION Joe’s Hamburger Shop sells 540 burgers each day. They sell hamburgers and turkey burgers. The hamburgers sold are 39 more than twice the turkey burgers sold. How many of each burger are sold a day? 40 adults and 26 kids went to see a movie on the opening screening and the revenue for the showing was $486.70. The next showing 20 adults and 31 kids went to see the same movie and the revenue was $332.45. How much was an adult ticket and how much was a kid ticket? At my uncle’s farm, he raises chickens and pigs. The number of chickens is four more than three times the number of pigs. If he has animals with 148 legs, then how many of each animal does he have on the farm? 353 people attend a local play at a private club. Members get tickets for $2.75, while non-members have to pay $6.50. If the total gate for the play came to $1762, how many members and non-members came to the play? Monica plans to save $5 per week and already has saved $25. Michael has $16 and plans to save $8 per week. In how many weeks will Monica and Michael have the same amount of money? How much money will they have saved? Quickie-Tricky Internet charges no monthly charge & $5 per hour to use their services. D.O.T. com Internet charges a $15 monthly charge plus $2 per hour to use their services. When will the companies charge the same amount? How much will they both charge? Hot Dog Health Club charges $25 to start and $50 per month. Fat-B-Gone Health Club charges a flat fee of $300. After how many months will the cost of the gyms be the same? How much will the cost be? The sum of two numbers is 51. The second number is six less than twice the first number. Find the two numbers. Jim runs a food cart and during a busy outdoor festival he sold $7343.75 worth of food. He sells hot dogs for $2.95 and steak sandwiches for $9.95. If he sold a total of 985 items that day, how many of each item did he sell? You have 15 coins in your pocket. The coins are either quarters or dimes. You have a total of $3.15. How many quarters and dimes do you have? The sum of twice Leann’s age and three times Morgan’s age is 30. Leann is 5 years older than Morgan. Find their ages. Alice is counting a cash register at the end of the night. She has $1015 in $5 bills and $10 bills. If she has 138 bills all together, how many of each type does she have? Horizon Wireless charges $50 plus $10 per GB of data used a month. Monkey Business charges $25 plus $15 per GB of data used a month. After how many GB of data will the cost be the same? How much will the total bill be? You are running a concession stand at the football game. Hotdogs sell for $2 each and sodas sell for $1 each. At the end of the night, you made a total of $478. The number of drinks sold was 10 more than the number of hotdogs sold. How many hotdogs and drinks did you sell? You are selling tickets at a high school football game. Student tickets cost $2 and adult tickets cost $3. You sell 1957 tickets and collect $5035. How many of each type tickets did you sell? Shantel has two job offers as a car sales person. At Crazy Cars, she will receive $600 plus a commission of 2% of her total sales for the month. At Sid’s Cars, she will receive $1000 plus a commission of 1.5% of her total sales. What is the total sales amount Shantel must meet each month to make the same income from either dealership? What will her income be from that amount of sales? Hot air balloon #1 is 10 meters about the ground, rising 15 meters per minute. Hot air balloon #2 is 150 meters above the air descending 20 meters per minute. In how many minutes will the balloons be the same height? How high will the balloons be at that time? There are 34 students in Mrs. Noell’s class. There are eight more boys than girls. How many boys and girls are in her class? ELIMINATION