LInear Systems Word Problems

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

• y = 6.80+.90x
  y = 7.30 + .65x

Tags

CCSS.HSA.CED.A.3

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 = 9.65x - 43
  y = 8.40x - 58

• y = 9.65x + 43
  y = 8.40x + 58

Tags

CCSS.8.EE.C.8C

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 

• x + y = 91
  14.80x + 17y = 6

• x + y = 6
  14.80x + 17y = 91

Tags

CCSS.HSA.CED.A.3

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have?  Which system best represents the situation? 

• x + y = 49
  20x + 50y = 1430

• x + y = 49
  x + y = 1430

Tags

CCSS.HSA.CED.A.3

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

• 5q + 2z = 1.32
  3q + 1z = 0.75

• 5q + 2z = 0.75
  3q + 1z = 1.32

Tags

CCSS.HSA.CED.A.3

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas 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 = 13
  3x + 7y = 13.5

• x + y = 4
  x - y = 6

Tags

CCSS.8.EE.C.8C

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3

• x + y = 33
  x = 2y - 3

Tags

CCSS.HSA.CED.A.3

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740

• S + A = 1740
  4S + 3A = 530

Tags

CCSS.HSA.CED.A.3

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 system of equations could be used? 

• x + y = 1550
  y = x + 4

• x + y = 1550
  y  = 4x

Tags

CCSS.8.EE.C.8C

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation? Use x as the number of haircuts; use y as the number of hair dyes.

• 2x + 2y = 315

  3x + 4y = 450

• 3x + 2y = 315

  2x + 4y = 450

Tags

CCSS.HSA.CED.A.3