Certainly! Let's solve the system of linear equations given by the problem to find the number of cars [tex]\( x \)[/tex] and trucks [tex]\( y \)[/tex] that the drama club washed.
We have the following system of equations:
1. [tex]\( x + y = 41 \)[/tex]
2. [tex]\( 5x + 8y = 250 \)[/tex]
We can solve this system step-by-step.
### Step 1: Express one variable in terms of the other using the first equation
From the first equation:
[tex]\[ x + y = 41 \][/tex]
We can solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[ y = 41 - x \][/tex]
### Step 2: Substitute this expression into the second equation
Now we substitute [tex]\( y = 41 - x \)[/tex] into the second equation [tex]\( 5x + 8y = 250 \)[/tex]:
[tex]\[ 5x + 8(41 - x) = 250 \][/tex]
### Step 3: Simplify and solve for [tex]\( x \)[/tex]
First, distribute the 8:
[tex]\[ 5x + 8 \cdot 41 - 8x = 250 \][/tex]
This simplifies to:
[tex]\[ 5x + 328 - 8x = 250 \][/tex]
Combine like terms:
[tex]\[ -3x + 328 = 250 \][/tex]
Subtract 328 from both sides to isolate terms involving [tex]\( x \)[/tex]:
[tex]\[ -3x = 250 - 328 \][/tex]
[tex]\[ -3x = -78 \][/tex]
Divide both sides by -3:
[tex]\[ x = \frac{-78}{-3} \][/tex]
[tex]\[ x = 26 \][/tex]
So, the number of cars [tex]\( x \)[/tex] washed is 26.
### Step 4: Find [tex]\( y \)[/tex] using the value of [tex]\( x \)[/tex]
Substitute [tex]\( x = 26 \)[/tex] back into the equation [tex]\( y = 41 - x \)[/tex]:
[tex]\[ y = 41 - 26 \][/tex]
[tex]\[ y = 15 \][/tex]
So, the number of trucks [tex]\( y \)[/tex] washed is 15.
### Conclusion
The drama club washed:
- [tex]\( 26 \)[/tex] cars, and
- [tex]\( 15 \)[/tex] trucks.
