Question

Three friends attended a carnival. John rode the rollercoaster twice, the bumper cars three times, and the Ferris wheel once. He used 42 tickets total. Darren rode the rollercoaster three times, the bumper cars once, and the Ferris wheel twice. He used 36 tickets. Shelley rode the rollercoaster once, the bumper cars twice, and the Ferris wheel 3 times. She used 32 tickets. Which system of equations matches the friends' night at the carnival?
A) 2x + 3y + z = 42
3x + y + 2z = 36
x + 2y + 3z = 32

B) 3x + 2y + z = 42
3x + y + 2z = 36
x + 2y + 3z = 32

C) 2x + 3y + z = 42
3x + 3y + 2x = 36
x + 2y + 3z = 32

D) 2x + 3y + z = 42
3x + y + 2z = 36
2x + 2y + 3z = 32

Answer 1

Answer:

The system of equations is the option A

Step-by-step explanation:

Let

x ------> the number of tickets for the roller-coaster

y ------> the number of tickets for the bumper

z ------> the number of tickets for the Ferris wheel

we know that

The system of equations is equal to

John

2x+3y+z=42

Darren

3x+y+2z=36

Shelley

x+2y+3z=32

therefore

The system of equations is the option A