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

This system of equations models the situation.

x + y =125

5x + 8y = 775

Solve the system to answer the questions.

How many premium car washes were ordered?

premium car washes



How many quick car washes were ordered?

quick car washes

Answer 1

To solve the system of equations, we have:

1. \( x + y = 125 \) (Equation 1)
2. \( 5x + 8y = 775 \) (Equation 2)

Where:

• \( x \) is the number of quick washes (at $5.00 each).
• \( y \) is the number of premium washes (at $8.00 each).

Step 1: Solve for \( y \) in terms of \( x \) using Equation 1

From Equation 1: \[ y = 125 - x \]

Step 2: Substitute \( y \) in Equation 2

Now substitute \( y \) in Equation 2: \[ 5x + 8(125 - x) = 775 \]

Step 3: Distribute and simplify

Expanding this gives: \[ 5x + 1000 - 8x = 775 \] Combine like terms: \[ -3x + 1000 = 775 \]

Step 4: Solve for \( x \)

Subtract 1000 from both sides: \[ -3x = 775 - 1000 \] \[ -3x = -225 \] Divide by -3: \[ x = 75 \]

Step 5: Find \( y \)

Now use the value of \( x \) to find \( y \): \[ y = 125 - x = 125 - 75 = 50 \]

Final Results

• Number of quick car washes (x): 75
• Number of premium car washes (y): 50

Thus, the number of premium car washes ordered is 50, and the number of quick car washes ordered is 75.