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 = 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

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
• t + n = 8
  t = 3n + 54

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 = 9.65 + 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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.REI.D.11

CCSS.HSA.SSE.A.1

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)

Tags

CCSS.8.EE.C.8B

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 = 6
  14.80x + 17y = 91
• x + y = 91
  14.80x + 17y = 6
• x + y = 6
  14.80y + 17x = 91
• x + y = 91
  14.80x+ 17y = 6

Tags

CCSS.HSA.CED.A.3

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:
x + y = 21
6x + 4y = 104

• (10, 11)
• (12, 9)
• (11, 10)
• (9, 12)

Tags

CCSS.8.EE.C.8C

What Are These Called?

• Penguins
• Minions
• Gru
• Animated Children

Tags

CCSS.RI.11-12.5

CCSS.RI.6.5

CCSS.RI.7.5

CCSS.RI.8.5

CCSS.RI.9-10.5

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 = 1430
  20x + 50y = 49
• x + y = 49
  10x + 5y = 1430 
• x + y = 49
  20x + 50y = 1430
• x + y = 49
  x + y = 1430

Tags

CCSS.HSA.CED.A.3

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother 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

Tags

CCSS.8.EE.C.8C

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
  1z = 0.75
• 5q + 2z = 1.32
  3q + 1z = 0.75
• q + z = 1.32
  q + z = 0.75
• 5q + 2z = 0.75
  3q + 1z = 1.32

Tags

CCSS.HSA.CED.A.3