To analyze Bob's two job offers and determine which job is better based on the number of hours worked, let's break down the payment structures.
Job 1: Hotel Job
- Pay: $18 per hour
- Transportation Allowance: $33 per month
Job 2: Restaurant Job
- Pay: $7.50 per hour
- Tips: Let's assume that the restaurant has 4 wait staff members total, as indicated in your equation \( \frac{50}{4} \). This means each worker gets $12.50 per hour ($50 in tips divided among 4 wait staff).
Total hourly earnings for the restaurant job can be calculated as: \[ 7.50 + 12.50 = 20 \] So, Bob earns $20 per hour at the restaurant when considering both hourly pay and tips.
Proposed equation:
The equation you provided: \[ 7.50h + \frac{50}{4}h = 18h + 33 \] This simplifies to: \[ 7.50h + 12.50h = 18h + 33 \] Combining like terms gives us: \[ 20h = 18h + 33 \] Subtracting \(18h\) from both sides results in: \[ 2h = 33 \] Solving for \(h\) gives: \[ h = 16.5 \] This means that if Bob works for more than 16.5 hours in a month, the restaurant job may have a better payout when considering tips.
Making an Inequality
To compare the two jobs and see which is better based on hours worked (\(h\)), we can set up the inequality as follows:
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The total pay for the hotel job after \(h\) hours is: \[ 18h + 33 \]
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The total pay for the restaurant job after \(h\) hours is: \[ 20h \]
Now we can create an inequality to determine when the restaurant job is better: \[ 20h > 18h + 33 \]
Subtract \(18h\) from both sides: \[ 2h > 33 \] Divide by 2: \[ h > 16.5 \]
Conclusion
If Bob works more than 16.5 hours in a month, the restaurant job becomes more financially beneficial than the hotel job. If he works less than or equal to 16.5 hours, the hotel job would be better, especially taking into account the transportation allowance.
Depending on the number of hours Bob intends to work, he can choose the most advantageous option based on this inequality.