Linear Word Problems with Matrices

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

Tags

CCSS.8.EE.C.8C

Using the previous question, how much did each ticket cost? Use matrix form to solve this on your calculator.

• 8 c

  14 s

• 8 s

  14 c

• 166 s

  218 c

• 218 c

  166 s

Tags

CCSS.HSA.REI.C.8

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? (This will be the top number on you 2x1 matrix solution)

• $5

• $10

• $15

• $20

Tags

CCSS.8.EE.C.8C

Solve: (round to nearest hundredth)

2x + 5y = 55

9x - 2y = 3

• (2.56, 9.97)

• (14.68, 12.75)

• (2.55, 9.98)

• (12.75, 14.86)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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 using matrices:

x + y = 21

6x + 4y = 104

• (10, 11)

• (12, 9)

• (11, 10)

• (9, 12)

Tags

CCSS.8.EE.C.8C

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Using matrices, what would be your solution as to how many nachos and soda he sold?

• (35, 52)

• (18, 69)

• ( 52, 35)

• (61, 26)

Tags

CCSS.8.EE.C.8C

The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. How many students were on each van and each bus?

• Van 43
  Bus 14
• Van 11
  Bus 21
• Van 14
  Bus 43
• Van 17
  Bus 45

Tags

CCSS.8.EE.C.8C

On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket using matrices on your calculator.

• Adult $13

  Child $5

• Adult $10

  Child $6

• Adult $8

  Child $16

• Adult $12

  Child $13

Tags

CCSS.8.EE.C.8C

The equations of two lines are 6x + y = 26 and y = 2x + 10. If the solution is (2, y), what is the value of y? 

• 14
• 4
• 6
• 2

Solve the following on your calculator:

(Round to nearest hundredth)

5x + 95y = 283

187x - 2y = 396

• (2.2, 2.9)

• (2.18, 2.85)

• (2.14, 2.86)

• (2.15, 2.87)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6