Question

Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes.


Let x represent the number of quick washes and let y represent the number of premium washes. Which system of linear equations represents the situation?
5x + 8y = 775 and x + y =125
5x – 8y = 125 and x + y = 775
5x + 8y = 775 and x – y = 125
5x – 8y = 125 and x – y = 775

Answer 1

Given:
quick washes = x ; $5
premium washes = y ; $8

x + y = 125
5x + 8y = 775

Correct answer is the 1st option.

x = 125 - y
5(125 - y) + 8y = 775
625 - 5y + 8y = 775
3y = 775 - 625
3y = 150
y = 150/3
y = 50 number of premium washes

x = 125 - 50
x = 75 number of quick washes

Answer 2

Let x represent the number of quick washes and let y represent the number of premium washes.

1. One quick wash costs $5, then x quick washes cost $5x.

One premium wash cost $8, then y premium washes cost $8y.

They made $775 from a combination of quick and premium washes, then in total they made $(5x+8y) that is $775. The first equation is

5x+8y=775.

2. They had washed 125 cars, x cars by quick wash and y cars by premium wash, that is x+y in total. Then tha second equation is

x+y=125.

Only option A represents the situation.