Gavin is working two summer jobs, making $14 per hour tutoring and $13 per hour landscaping. Last week Gavin worked a total of 10 hours and earned a total of $137. Determine the number of hours Gavin worked tutoring last week and the number of hours he worked landscaping last week.

Question

Answer
Attempt 1 out of 2

Gavin worked
hours tutoring and
hours landscaping.

Answer 1

Let \( t \) be the number of hours Gavin worked tutoring and \( l \) be the number of hours he worked landscaping. We can set up the following two equations based on the information provided:

1. The total number of hours worked: \[ t + l = 10 \]

2. The total earnings from both jobs: \[ 14t + 13l = 137 \]

We can solve these equations simultaneously. We start by solving the first equation for \( l \): \[ l = 10 - t \]

Next, we substitute this expression for \( l \) into the second equation: \[ 14t + 13(10 - t) = 137 \]

Now, distribute the \( 13 \): \[ 14t + 130 - 13t = 137 \]

Combine like terms: \[ t + 130 = 137 \]

Now, isolate \( t \): \[ t = 137 - 130 \] \[ t = 7 \]

Now that we have \( t \), we can find \( l \) using the first equation: \[ l = 10 - t = 10 - 7 = 3 \]

Thus, Gavin worked:

• 7 hours tutoring
• 3 hours landscaping

Final Answer: Gavin worked 7 hours tutoring and 3 hours landscaping.