Solving Systems of Equations with 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

Tags

CCSS.HSA.CED.A.3

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

Tags

CCSS.HSA.CED.A.3

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

Tags

CCSS.8.EE.C.8C

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

Tags

CCSS.8.EE.C.8C

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

Tags

CCSS.HSA.CED.A.3

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

Tags

CCSS.8.EE.C.8C

Some students want to order shirts with their school logo. One company charges a total of $9.65 per shirt plus a setup fee of $43. Another company charges a total of $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

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? (Where will the two lines touch?)

• (1, 12)

• (3, 19)

• (5, 25)

Tags

CCSS.8.EE.C.8B

There are 15 animals in a barn.  These animals are horses (x) and chickens (y).  There are 44 legs in all.  Which system of equations represents the situation?

• x + y = 15
  4x + 2y = 44

• 4x + 2y = 15
  x + y = 44

• x = 2y + 44
  4x = y + 15

• 2x - 4y = 44
  x - y = 15

Tags

CCSS.8.EE.C.8C

Nancy went to the grocery story.  On Monday she purchased 4 apples (x) and 6 bananas (y) for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6

• x + y = 4
  x - y = 6

• 4x + 6y = 13
  3x + 7y = 13.5

• 4x - 6y = 13
  3x - 7y = 13.5

Tags

CCSS.8.EE.C.8C