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Systems of Equations Word Problems

Choosing the best method

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Systems of Equations Word Problems

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  1. Wednesday 16th

  2. Best Method- ________________ Name- _____________________ Warm-Up Best Method- ________________ Best Method- ________________

  3. Best Method- Substitution

  4. Best Method- Graphing

  5. Let’s try some word problems!!

  6. Let’s try this one together. Severna Park Middle school music department purchases sandwiches and drinks for their end of the year picnic. Each sandwich cost $5 and each drink cost $2. A total of 56 items were purchased for $200. If s = sandwiches and d = drinks, which system represents this situation? • s + d = 56 5s + 2d = 200 c. s + d = 56 2s + 5d = 200 d. s - d = 56 5s + 2d = 200 b. s + d = 200 5s + 2d = 56

  7. Let’s try this one together. Severna Park Middle school music department purchases sandwiches and drinks for their end of the year picnic. Each sandwich cost $5 and each drink cost $2. A total of 56 items were purchased for $200. If s = sandwiches and d = drinks, which system represents this situation? • s + d = 56 5s + 2d = 200 c. s + d = 56 2s + 5d = 200 d. s - d = 56 5s + 2d = 200 b. s + d = 200 5s + 2d = 56

  8. Let’s try this one together. The price of Verizon cellular phone plan is based on peak and nonpeak service. Ms. White used 45 peak minutes and 50 nonpeak minutes and was charged $27.75. The same month, Mrs. Reynolds used 70 peak minutes and 30 non-peak minutes for a total of charge of $36. If p = peak minutes and n = non-peak minutes, which system represents this situation? • 50p - 45n = 36 70p + 30n = 27.75 c. 50p - 45n = 36 30p + 70n = 27.75 d. 45p + 50n = 27.75 70p + 30n = 36 b. 70p + 30n = 27.5 50p + 45n = 36

  9. Let’s try this one together. The price of Verizon cellular phone plan is based on peak and nonpeak service. Ms. White used 45 peak minutes and 50 nonpeak minutes and was charged $27.75. The same month, Mrs. Reynolds used 70 peak minutes and 30 non-peak minutes for a total of charge of $36. If p = peak minutes and n = non-peak minutes, which system represents this situation? • 50p - 45n = 36 70p + 30n = 27.75 c. 50p - 45n = 36 30p + 70n = 27.75 d. 45p + 50n = 27.75 70p + 30n = 36 b. 70p + 30n = 27.5 50p + 45n = 36

  10. Let’s try this one together. Mrs. Simonds and Mrs. Schauppner went to a baseball game. Mrs. Simonds bought 6 hotdogs and 2 sodas that cost $15.00. Mrs. Schauppner bought 9 hot dogs and 4 sodas that cost $24. If h = hot dogs and s = sodas, which system represents this situation? • 6h + 2s = 24 9h - 4s= 15 c. 6h + 2s = 24 4h + 9s= 15 d. 9h + 4s = 15 6h + 2s= 24 b. 6h + 2s = 15 9h + 4s= 24

  11. Let’s try this one together. Mrs. Simonds and Mrs. Schauppner went to a baseball game. Mrs. Simonds bought 6 hotdogs and 2 sodas that cost $15.00. Mrs. Schauppner bought 9 hot dogs and 4 sodas that cost $24. If h = hot dogs and s= sodas, which system represents this situation? • 6h + 2s = 24 9h - 4s= 15 c. 6h + 2s = 24 4h + 9s= 15 d. 9h + 4s = 15 6h + 2s= 24 b. 6h + 2s = 15 9h + 4s= 24

  12. We guide with them. Mrs. Newton and her friend headed to Taco Bell. Mrs. Newton bought 2 tacos and 1 burrito for 7.25. Her friend buys 3 tacos and 2 burritos for $13.25. Variables: Write a system of equations to represent the situation. Solve the system you wrote to determine the cost of a taco and the coast of a burrito.

  13. t = tacos b= burrito Mrs. Newton and her friend headed to Taco Bell. Mrs. Newton bought 2 tacos and 1 burrito for 7.25. Her friend buys 3 tacos and 2 burritos for $13.25. Variables: Write a system of equations to represent the situation. 2t + b =7.25 3t +2b = 13.25 Solve the system you wrote to determine the cost of a taco and the coast of a burrito. 2t + b = 7.25 2t + b = 7.25 3t +2b = 13.25 2(1.25) + b = 7.25 2.50 +b = 7.25 -2(2t + b = 7.25) -4t -2b = -14.5 -2.50 -2.50 3t +2b = 13.25 3t + 2b = 13.25b = 4.75 -(-t = -1.25) t = 1.25 It cost $1.25 for a taco and $4.75 for one burrito. (1.25, 4.75)

  14. Let’s write a system: A youth group and their leaders visited Downtown Annapolis in Maryland. Two adults and 5 students in one van paid $77 for the Grand Avenue Tour of the city. Two adults and 7 students in a second van paid $95 for the same tour. Find the adult price and the student price of the tour. Variables: System of equations:

  15. Let’s write a system: A youth group and their leaders visited Downtown Annapolis in Maryland. Two adults and 5 students in one van paid $77 for the Grand Avenue Tour of the city. Two adults and 7 students in a second van paid $95 for the same tour. Find the adult price and the student price of the tour. Variables: x = the price of adult ticket y= the price of a student ticket System of equations: 2x +5y = 77 2x + 5(9)=77 2x +45=77 -45 -45 2x = 32 x = 16 2x + 5y=77 2x +7y = 95 2x + 5y=77 2x + 5y=77 -(2x +7y = 95) -2x -7y =-95 The price of an adult ticket is $16 and the price of a student ticket is $9. -2y = 18 y =9

  16. Task #1 The Box Dilemma Small boxes contain DVDs, and large boxes contain one gaming machine. • Three large boxes of gaming machines and a small box of DVDs weighs 48 pounds. • Three large boxes of gaming machines and five small boxes of DVDs weigh 72 pounds. • How much does each box weigh? Use this system of equations to solve where x represents the number of small boxes and y represents the number of large boxes. 3y + 1x = 48 3y + 5x = 72

  17. Task #1 The Box Dilemma Small boxes contain DVDs, and large boxes contain one gaming machine. • Three large boxes of gaming machines and a small box of DVDs weighs 48 pounds. • Three large boxes of gaming machines and five small boxes of DVDs weigh 72 pounds. • How much does each box weigh? Use this system of equations to solve where x represents the number of small boxes and y represents the number of large boxes. 3y + 1x = 48 3y + 5x = 72 3y + 1x = 48 3y +1(6)=48 3y +6 = 48 -6 -6 3y = 42 y= 14 3y + 1x = 48 3y + 1x = 48 -(3y + 5x = 72) -3y -5x = -72 -4x = -24 x=6 There are 6 small boxes and 14 large boxes.

  18. Task # 2 Movie Tickets Tickets for a matinee are $5 for children and $8 for adults. • The theater sold a total of 142 tickets for one matinee. • Ticket sales were $890. • How many of each type of ticket did the theater sell? Use this system of equations to solve where x represents the number of children tickets and y represents the number adult tickets. x + y = 142 5x + 8y = 890

  19. Movie Tickets Tickets for a matinee are $5 for children and $8 for adults. • The theater sold a total of 142 tickets for one matinee. • Ticket sales were $890. • How many of each type of ticket did the theater sell? Use this system of equations to solve where x represents the number of children tickets and y represents the number adult tickets. x + y = 142 5x + 8y = 890 Task # 2 x + y = 142 x + (60) = 142 -60 -60 x = 82 -5(x + y = 142) -5x -5y = -710 5x + 8y = 890 5x + 8y = 890 3y = 180 y = 60 There were 82 children tickets and 60 adult tickets sold for the movie.

  20. Task # 3 Popcorn and Candy Some friends went to the local movie theater and bought 4 large buckets of popcorn and 6 boxes of candy. • The total for the snacks was $46.50. • The last time you were at the theater, you bought 2 large buckets of popcorn and 4 boxes of candy, and the total was $27.00 • What is the cost of a bucket of one bucket of popcorn and one box of candy? Use this system of equations to solve where x represents the cost of the popcorn and y represents the cost of candy. 4x + 6y = 46.50 2x + 4y = 27.00

  21. Task # 3 Popcorn and Candy Some friends went to the local movie theater and bought 4 large buckets of popcorn and 6 boxes of candy. • The total for the snacks was $46.50. • The last time you were at the theater, you bought 2 large buckets of popcorn and 4 boxes of candy, and the total was $27.00 • What is the cost of a bucket of one bucket of popcorn and one box of candy? Use this system of equations to solve where x represents the cost of the popcorn and y represents the cost of candy. 4x + 6y = 46.50 2x + 4y = 27.00

  22. Task # 4 Savings Time Andre and Noah started tracking their savings at the same time. • Andre started with $15 and deposits $5 per week. • Noah started with $2.50 and deposits $7.50 per week. • When will Andre and Noah have saved the same amount of money? • How much money will each boy save during that time period? Use this system of equations to solve where x represents the number of weeks and y represents the amount of money saved. y = 5x + 15 y = 7.50x + 2.50

  23. Task # 4 Savings Time Andre and Noah started tracking their savings at the same time. • Andre started with $15 and deposits $5 per week. • Noah started with $2.50 and deposits $7.50 per week. • When will Andre and Noah have saved the same amount of money? • How much money will each boy save during that time period? Use this system of equations to solve where x represents the number of weeks and y represents the amount of money saved. y = 5x + 15 y = 7.50x + 2.50 5x +15= 7.50x +2.50 -5x -5x 15 = 2.50x + 2.50 -2.5 -2.50 12.5 = 2.50x 5 = x Each boy will have $26 in 5 weeks. y = 5x +1 y = 5(5) +1 y= 25 +1 y = 26

  24. Task # 5 A school is selling t-shirts and sweatshirts for a fundraiser. • The table shows the number of t-shirts and the number of sweatshirts in each of three recent orders. • The total cost of orders A and B are given. • Each t-shirt has the same cost, and each sweatshirt has the same cost. • What is the cost of a t-shirt and a sweatshirt? Use this system of equations to solve where x represents the cost of the t-shirt and y represents the cost of the sweatshirt. 2x + 2y = 38 3x + y = 35

  25. Task # 5 A school is selling t-shirts and sweatshirts for a fundraiser. • The table shows the number of t-shirts and the number of sweatshirts in each of three recent orders. • The total cost of orders A and B are given. • Each t-shirt has the same cost, and each sweatshirt has the same cost. • What is the cost of a t-shirt and a sweatshirt? Use this system of equations to solve where x represents the cost of the t-shirt and y represents the cost of the sweatshirt. 2x + 2y = 38 3x + y = 35 2x +2y = 38 2x + 2y = 38 -2(3x + y = 35) -6x -2y = -70 -4x = - 32 x = 8 2x +2y = 38 2 (8) + 2y = 38 16 + 2y = 38 -16 -16 2y= 22 y = 11 It cost $8 for a t-shirt and $11 for a sweatshirt.

  26. Task # 6 Sums and Differences The sum of two whole numbers is 361, and the difference between the two numbers is 173. What are the two numbers? Use this system of equation and elimination to solve where x represents the larger whole number and y represents the smaller whole number. x + y = 361 x–y = 173

  27. Task # 6 Sums and Differences The sum of two whole numbers is 361, and the difference between the two numbers is 173. What are the two numbers? Use this system of equation and elimination to solve where x represents the larger whole number and y represents the smaller whole number. x + y = 361 x–y = 173 x + y = 361 267 + y = 361 -267 -267 y = 94 x + y = 361 x - y = 173 2x = 534 x = 267 The larger number is 267 and the smaller whole number is 94.

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