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?

We are given that Jayden's paychecks from two jobs were the same after working the same amount of hours, $ h $, at each job. Let's define the total earnings from each job and set up an equation.

### Step 1: Define the total earnings for each job
1. **Server Job**:
   - Hourly rate: $9.64 per hour.
   - Tips: $82.35.
   - Total earnings for $ h $ hours at the server job:
     \[
     \text{Earnings from server job} = 9.64h + 82.35
     \]

2. **Jewelry Store Job**:
   - Hourly rate: $14.86 per hour.
   - Sales bonuses: $17.10.
   - Total earnings for $ h $ hours at the jewelry store:
     \[
     \text{Earnings from jewelry store job} = 14.86h + 17.10
     \]

### Step 2: Set the earnings equal to each other
Since the paychecks were the same, we can set the total earnings from both jobs equal to each other:
\[
9.64h + 82.35 = 14.86h + 17.10
\]

### Step 3: Solve for $ h $
First, subtract $ 9.64h $ from both sides:
\[
82.35 = 5.22h + 17.10
\]
Next, subtract 17.10 from both sides:
\[
82.35 - 17.10 = 5.22h
\]
\[
65.25 = 5.22h
\]
Now, solve for $ h $ by dividing both sides by 5.22:
\[
h = \frac{65.25}{5.22} \approx 12.5
\]

### Conclusion:
Jayden worked approximately **12.5 hours** at each job when both paychecks were the same.

Would you like more details on any part of this solution?

### Related Questions:
1. What would Jayden's total earnings be from both jobs after working 12.5 hours?
2. How much more does Jayden earn per hour at the jewelry store compared to the server job?
3. If Jayden worked 15 hours at the server job, what would his paycheck be?
4. How would the solution change if the tips or bonuses increased?
5. What if Jayden worked different hours at each job—how would we set up the equation?

### Tip:
When comparing two different income sources, always break down earnings into hourly wages and additional income (like tips or bonuses) to set up equations effectively!

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?

Discover how to solve a real-life problem involving linear equations. Jayden worked two jobs with different hourly rates and bonuses, but his paychecks were the same. Learn how to calculate the hours worked at each job using algebraic methods. This step-by-step guide is ideal for students in Grades 8-10.

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