Question

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.
Graph a system of equations that represents this story.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
7
8
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12
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15
x
y
Cars washed
Larger vehicles washed
Car wash fundraiser
vehiclesdollars
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.