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 the number of hours Jayden worked at each job be represented by $ h $.

### Pay from the server job:
Jayden earns $9.64 per hour and also received $82.35 in tips. So, his total earnings from the server job can be written as:
\[
\text{Total earnings from server job} = 9.64h + 82.35
\]

### Pay from the jewelry store job:
Jayden earns $14.86 per hour and also received $17.10 in sales bonuses. So, his total earnings from the jewelry store job can be written as:
\[
\text{Total earnings from jewelry store job} = 14.86h + 17.10
\]

### Since the paychecks were the same, we can set the two expressions equal to each other:
\[
9.64h + 82.35 = 14.86h + 17.10
\]

### Solving for $ h $:

1. Subtract $ 9.64h $ from both sides:
\[
82.35 = (14.86h - 9.64h) + 17.10
\]
\[
82.35 = 5.22h + 17.10
\]

2. Subtract 17.10 from both sides:
\[
82.35 - 17.10 = 5.22h
\]
\[
65.25 = 5.22h
\]

3. Divide both sides by 5.22:
\[
h = \frac{65.25}{5.22} \approx 12.5
\]

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

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

Here are some related questions you can explore:
1. How much did Jayden earn in total from each job?
2. How much of Jayden's total earnings came from tips and bonuses?
3. How would the situation change if Jayden worked more hours at the jewelry store?
4. What if Jayden had earned more tips as a server? How would that affect the number of hours worked?
5. If Jayden worked 15 hours at each job, how would his total paychecks differ?

**Tip:** When solving equations with variables, simplify terms step by step to avoid errors.

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?

Learn how to solve a linear equation to find out how many hours Jayden worked at two different jobs when both paychecks were the same. This problem covers algebraic concepts, including solving for variables and equating two earnings expressions. Suitable for Grades 8-10.

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