Systems of Equations Word Problems

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. Which equations represents the system that could be used? Pick 2.

• 3s + 1c = 38

• 3s + 2c = 52

• s + c = 52

• 3s + 3c = 38

Last season, two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which 2 equations could be used?

• x + y = 1550

• y = x + 4

• y - x = 1550

• y = 4x

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which 2 equations could be used to find the exact number of dimes and nickels?

• d + n = 6.60

• 10d + 5n = 6.60

• d + n = 80

• .10d + .05n = 6.60

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

• 5c + 10d = 14.25

• 10c + 5d = 16.50

• c + d = 10

• c + d = 5

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping.The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which equations could be used to find the number of toppings when both companies cost the same amount?

• y = 6.80 + .65x

• y = 7.30 + .65x

• y = 6.80+.90x

• y + .65x = 7.30

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos

  m: # of glasses of milk

• t: Cost of each taco

  m: Cost of each glass of milk

• t: total cost

  m: # of food items

• t: Cost of each glass of milk

  m: Cost of each taco

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which 2 linear equations could be used to determine the price of each book?

• t + n = 54

• n = 3t + 8

• t = 3n + 8

• t = 3n + 54

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which 2 equations represent the situation above?

• y = 9.65 + x

• y = 9.65x + 43

• y = 8.40x

• y = 8.40x + 58

Lisa and Tammy are selling items at the craft show. Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount?

• (1, 12)

• (3, 19)

• (5, 25)

• (0, 10)

Kim is selling tickets to a dance competition. On the first day she sold 8 adult tickets and 3 child tickets for $122. On the second day she sold 4 adult tickets and 4 child tickets for $76. Write the system of equations.

• 8a + 4a = 122

  3c + 4c = 76

• 8a -3c = 122

  4a-4c=76

• 3c -4c = 76

  8a - 4a = 122

• 8a + 3c = 122

  4a + 4c = 76