Solving pairs of linear equations in two variables

Yellowstone National Park is a popular field trip destination. The senior class of High School A and the senior class of High School B are all planning on going there. High School A rented and filled 8 vans and 3 buses with 208 students. High School B rented and filled 14 vans and 12 buses with 580 students. Each van and each bus carried the same number of students. How many students were in each van, and how many in each bus?

• Van: 14, Bus: 32

• Van: 20, Bus: 16

• Van: 32, Bus: 14

• Van: 20, Bus: 16

• Van: 16, Bus: 20

Roman mowed his next door neighbor’s lawn for a handful of dimes and nickels, 280 coins in all.  Upon completing the job he counted out the coins and it came to $26.60.  Find the exact number of dimes and nickels.

• nickels 120

  dimes 160

• nickels 220

  dimes 60

• nickels 28

  dimes 252

• nickels 42

  dimes 138

In a pasture are horses and chickens if there are a total of 28 animals and 80 legs how many horses are there?

• 10 horses

• 16 horses

• 12 horses

• 18 horses

• Caroline can order 12 games from Plan A & 6 games from Plan B.

• If Caroline orders 12 games each month, both plans will cost $6.

• Caroline can order 6 games from Plan A & 12 games from Plan B.

• If Caroline orders 6 games each month, both plans will cost $12.

Kayla's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 11 senior citizen tickets and 10 child tickets for a total of $252. The school took in $108 on the second day by selling 7 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

• senior citizen ticket: $12

  child ticket: $12

• senior citizen ticket: $14

  child ticket: $8

• senior citizen ticket: $18

  child ticket: $17

• senior citizen ticket: $5

  child ticket: $9

Michelangelo decided to order Pizza Hut last night. He purchased 3 pizzas and 2 orders of breadsticks for a total of $29.50. Donatello ordered 2 pizzas and 3 orders of breadsticks last Sunday for a total of $23. Set up a system. Let "p" represent the price per pizza and "b" represent the price of an order of breaksticks.

• 3p + 2b = 29.50
  2p + 3b = 23
• 3p + 2b = 23
  2p + 3b = 29.50
• 3b + 2p = 29.50
  2b + 3p = 23
• 5bp = 29.50
  5bp = 23

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

• x + y = 78.50

• 1.50x + 0.50y = 87

• 1.50x + 0.50y = 78.50

  x + y = 87

• x + 0.50y = 87

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.  How long does it take her to do a haircut?
3x + 2y = 315
2x + 4y = 450

• 45 minutes

• 90 minutes

• 60 minutes

• 30 minutes

John was 20 feet away and was running 5 feet per minute. Alex was 50 feet away and was 3 feet per minute. Write a system of two equations for this situation?

• y = 5x + 20

  y = 3x + 50

• y = 20x + 5

  y = 50x + 3

• y = 5x + 50

  y = 2x + 20

• y = 50x + 5

  y = 20x + 3