Jayden has two jobs. One week he noticed his paychecks were the same after working the same amount of hours at both jobs. As a server he earned $9.64
 per hour plus $82.35
 in tips. Working at a jewelry store he earned $14.86
 per hour plus $17.10
 in sales bonuses.  

 

How many hours did Jayden work at each job when both of the paychecks were the same?

Let's denote the number of hours Jayden worked at each job as $ h $.

### Server Job:
- Hourly wage: $ \$9.64 $ per hour
- Tips: $ \$82.35 $
- Total earnings: $ 9.64h + 82.35 $

### Jewelry Store Job:
- Hourly wage: $ \$14.86 $ per hour
- Sales bonus: $ \$17.10 $
- Total earnings: $ 14.86h + 17.10 $

Since Jayden's paychecks were the same for both jobs, we can set the total earnings equal to each other:

\[
9.64h + 82.35 = 14.86h + 17.10
\]

### Solving for $ h $:

1. Subtract $ 9.64h $ from both sides:

\[
82.35 = 5.22h + 17.10
\]

2. Subtract $ 17.10 $ from both sides:

\[
65.25 = 5.22h
\]

3. Divide both sides by $ 5.22 $:

\[
h = \frac{65.25}{5.22} \approx 12.5
\]

Jayden worked **12.5 hours** at each job.

Would you like any more details or have any questions? Here are five related questions to consider:

1. What would Jayden's total earnings be at each job after 12.5 hours?
2. How would the required hours change if his tips at the server job were doubled?
3. What would happen if Jayden received no tips or bonuses? How would the hours compare then?
4. If Jayden worked 5 more hours at the jewelry store, how would his total earnings compare?
5. How many hours would Jayden need to work at the jewelry store alone to match his total earnings from both jobs?

**Tip:** When solving equations involving the same variable on both sides, start by isolating the variable on one side to simplify the equation.

Explore how to solve a problem where Jayden's paychecks from two jobs became equal after working a certain number of hours. Understand the calculations involving hourly wages, tips, and bonuses.

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