Solving Word Problems with Systems of Equations

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 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

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 equation represents the number of shirts when both companies charge the same amount?

• y = 9.65 + x
  y = 8.40 + x

• y = 9.65x + 43
  y = 8.40x + 58

• y =9.65x
  y = 8.40x

• y = 9.65x - 43
  y = 8.40x - 58

The sum of Mr. Micklow and Ms. Craft's age is 55.  The difference is 3.  
Solve:
x + y = 55
x - y = 3

• (26, 23)

• (26, 29)

• (29, 26)

• (29, 32)

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

Last season two running backs on the Steelers football team rushed a combined (both running backs) 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

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 (all) the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels? (Hint: How much are the coins worth?)

• d + n = 6.60

  .10d + .05n = 80

• d + n = 80

  d + n = 6.60

• d + n = 80

  .10d + .05n = 6.60

A large pizza at Palanzio’s Pizzeria (c) costs $6.80 plus $0.90 for each topping.The cost of a large cheese pizza at Guido’s Pizza (c) 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

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

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the (total) 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

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