The Cherry Creek Middle School band held a car wash to raise money for new uniforms. The band charged $10 for cars and $15 for larger vehicles, like vans or SUVs. In the first hour of the car wash, band members washed a total of 10 vehicles and raised $120 toward their uniforms.

Question

Graph a system of equations that represents this story.
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Now complete the sentence.
The band washed cars and larger vehicles in the first hour of the car wash.
Submit

Answer 1

To model the given situation, we can define our variables and create a system of equations.

Let:

• \( x \) = number of cars washed
• \( y \) = number of larger vehicles (vans or SUVs) washed

From the information provided, we have the following two equations:

1. The total number of vehicles washed: \[ x + y = 10 \]

2. The total amount of money raised from washing the vehicles: \[ 10x + 15y = 120 \]

Now, we can graph this system of equations.

First Equation: From \( x + y = 10 \):

• When \( x = 0 \), \( y = 10 \) → Point (0, 10)
• When \( y = 0 \), \( x = 10 \) → Point (10, 0)

Second Equation: From \( 10x + 15y = 120 \):

• When \( x = 0 \): \[ 15y = 120 \implies y = 8 \quad \text{→ Point (0, 8)} \]
• When \( y = 0 \): \[ 10x = 120 \implies x = 12 \quad \text{→ Point (12, 0)} \]

To find the intersection of these two lines, we can simultaneously solve the equations.

Using the first equation \( y = 10 - x \), substitute into the second equation:

\[ 10x + 15(10 - x) = 120 \] \[ 10x + 150 - 15x = 120 \] \[ -5x + 150 = 120 \] \[ -5x = -30 \] \[ x = 6 \]

Now substitute \( x = 6 \) back into the first equation: \[ 6 + y = 10 \implies y = 4 \]

Conclusion: The band washed 6 cars and 4 larger vehicles in the first hour of the car wash.

So to complete the sentence: The band washed 6 cars and 4 larger vehicles in the first hour of the car wash.