Question

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.
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.