Systems 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? 

• 1s + 3c = 38
  2s + 3c = 52
• 3s + 1c = 38
  3s + 2c = 52
• s + c = 38
  s + c = 52
• 3s + 3c = 38
  1s + 2c = 52

Last season two running backs on the WCHS 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 system of equations could be used? 

• x + y = 1550
  y  = 4x
• x + y = 1550
  y = x + 4
• y - x = 1550
  y = 4x
• y = 1550 + x
  y = x + 4

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 system of equations could be used to find the exact number of dimes and nickels? 

• d + n = 6.60
  .10d + .05n = 80
• d + n = 80
  d + n = 6.60
• d + n = 80
  .10d + .05n = 6.60
• d + n = 80
  .05d + .10n = 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? 

• 10c + 5d = 14.25
  5c + 10d = 16.50
• 10c + 5d = 16.50
  5c + 10d = 14.25
• c + d = 10
  5c + 10d = 16.50
• c + d = 5
  5c + 10d = 16.50

A large pizza at Pizzi Inn 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 system of equations could be used to find the number of toppings when both companies cost the same amount? 

• y = 6.80 + .65x
  y=7.30+.90x
• x + y = 6.80
  x + y = 7.30
• y = 6.80+.90x
  y = 7.30 + .65x
• y + .90x = 6.80
  y + .65x = 7.30

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 system of linear equations could be used to determine the price of each book?

• t + n = 54
  t = 3n + 8
• t + n = 54
  n = 3t + 8
• t + n = 54
  t = 3n - 8
• t + n = 8
  t = 3n + 54

The sum of Mrs. LaRoque's and Mrs. Murphy's ages is 61. The difference is 7. What are their ages?

• 31 and 31

• 54 and 7

• 27 and 34

• 21 and 40

Wyatt and Emerson went shopping at a back-to-school sale where all shirts and shorts were the same price. Wyatt spent $175 on 7 new shirts and 7 pairs of shorts. Emerson purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

• $5

• $10

• $15

• $20

Chase is running a concession stand at a WCHS soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, Chase made a total of $78.50 and sold a total of 87 nachos and sodas combined. How much of each item did he sell?

• 35 nachos, 52 sodas

• 18 nachos, 69 sodas

• 52 nachos, 35 sodas

• 61 nachos, 26 sodas

Gracie sells tickets for admission to the WCHS school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. She sold 21 tickets total. How many of each type of ticket did Gracie sell?

• 10 adults, 11 children

• 12 adults, 9 children

• 11 adults, 10 children

• 9 adults, 12 children