Jackson is working two summer jobs, making $10 per hour washing cars and $12 per hour landscaping. Last week Jackson worked a total of 14 hours and earned a total of $152. Determine the number of hours Jackson worked washing cars last week and the number of hours he worked landscaping last week.

Answer 1

Let \( x \) be the number of hours Jackson worked washing cars, and \( y \) be the number of hours he worked landscaping. We have the following two equations based on the information given:

1. The total number of hours worked: \[ x + y = 14 \]

2. The total earnings: \[ 10x + 12y = 152 \]

We can solve this system of equations step-by-step. First, let's solve the first equation for \( y \):

\[ y = 14 - x \]

Next, substitute this expression for \( y \) into the second equation:

\[ 10x + 12(14 - x) = 152 \]

Now, distribute \( 12 \) in the equation:

\[ 10x + 168 - 12x = 152 \]

Combine like terms:

\[ -2x + 168 = 152 \]

Next, isolate \( x \) by subtracting \( 168 \) from both sides:

\[ -2x = 152 - 168 \] \[ -2x = -16 \]

Dividing both sides by \( -2 \) gives:

\[ x = 8 \]

Now, substitute \( x = 8 \) back into the equation for \( y \):

\[ y = 14 - x = 14 - 8 = 6 \]

Thus, Jackson worked 8 hours washing cars and 6 hours landscaping. We can summarize our findings:

• Hours washing cars: \( 8 \)
• Hours landscaping: \( 6 \)

To verify, we can check his total earnings:

\[ 10(8) + 12(6) = 80 + 72 = 152 \]

Both conditions are satisfied. Therefore, the final answer is:

\[ \text{Jackson worked 8 hours washing cars and 6 hours landscaping.} \]