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.

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**.