Kayla is working two summer jobs, making \$10 per hour lifeguarding and \$21 per hour tutoring. Last week Kayla worked 4 times as many hours tutoring as she worked lifeguarding and earned a total of $$ \$ 188 $$. Write a system of equations that could be used to determine the number of hours Kayla worked lifeguarding last week and the number of hours she worked tutoring last week. Define the variables that you use to write the system. Answer attempt 1 out of 2

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UpStudy AI · Accepted Answer

To determine the number of hours Kayla worked in each job last week, we can set up a system of equations based on the information provided.

### Define the Variables:
- **$$ L $$**: The number of hours Kayla worked **lifeguarding** last week.
- **$$ T $$**: The number of hours Kayla worked **tutoring** last week.

### System of Equations:

1. **Relationship Between Hours Worked:**
   
   Kayla worked **4 times as many hours tutoring** as she did lifeguarding.
   
   $$
   T = 4L
   $$

2. **Total Earnings:**
   
   Kayla's total earnings from both jobs last week were **\$188**. She earns **\$10 per hour** lifeguarding and **\$21 per hour** tutoring.
   
   $$
   10L + 21T = 188
   $$

### Summary:

$$
\begin{cases}
T = 4L \
10L + 21T = 188
\end{cases}
$$

**Where:**
- $$ L $$ = Hours worked lifeguarding
- $$ T $$ = Hours worked tutoring

This system of equations can be solved simultaneously to find the exact number of hours Kayla worked in each job last week.
Let $$ L $$ be the number of hours Kayla worked lifeguarding and $$ T $$ be the number of hours she worked tutoring. The system of equations is: 1. $$ T = 4L $$ 2. $$ 10L + 21T = 188 $$

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