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.

Question

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

To represent the situation using a system of linear equations, we need to consider the two pieces of information given: the total number of cars washed and the total amount of money made.

1. Let \( x \) represent the number of quick washes (which cost $5 each) and \( y \) represent the number of premium washes (which cost $8 each).
2. From the problem, we know:
   • The total number of cars washed (quick and premium) is 125: \[ x + y = 125 \]
   • The total amount of money made from these washes is $775: \[ 5x + 8y = 775 \]

Putting this information into the form of a system of linear equations, we have:

\[ \begin{align*}

1. & \quad x + y = 125 \
2. & \quad 5x + 8y = 775 \end{align*} \]

Thus, the correct system of equations that represents the situation is:

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