to help pay for tuition a college student plans to work in. the evening and on weekends he has been offered two part-time jobs working in the guest service department at a hotel and waiting tables at a popular restaurant.

Question

the job at the hotel pays 18$ a hour and offers 33$ in transportation allowance per month
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the job at the restaurant pays 7.50 an hour plus tips the entire waitstaff typically collects about 50$ in tips each hour tips are divided equally between 4 waitstaff members who share a shift

the equation 7.50h+50/4h=18h+33 represent the possible constraint about a situation

what do you know? what if a student works less hours which job is better make a inequality

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Answer 1

To analyze the situation, we need to break down the earnings for each job based on the number of hours worked.

Job 1: Hotel Guest Service Department

• Pay: $18 per hour
• Transportation allowance: $33 per month

Earnings for h hours worked: \[ \text{Earnings}_\text{hotel} = 18h + 33 \]

Job 2: Restaurant Waitstaff

• Pay: $7.50 per hour
• Tips: $50 divided by 4 waitstaff members = $12.50 per hour (average tip earnings per person)

Total pay per hour for the restaurant: \[ \text{Earnings}_\text{restaurant} = 7.50h + 12.50h = 20h \]

Creating the Equation

From the problem statement, the equation \( 7.50h + \frac{50}{4}h = 18h + 33 \) can be simplified:

1. \( 50/4 = 12.50 \), so the equation becomes: \[ 7.50h + 12.50h = 18h + 33 \]
2. Combine like terms on the left: \[ 20h = 18h + 33 \]
3. Rearranging gives us: \[ 20h - 18h = 33 \] \[ 2h = 33 \] \[ h = 16.5 \]

This means that if the student works 16.5 hours, both jobs would yield the same earnings.

Creating the Inequality

Now let's consider what happens if the student works fewer hours.

To find out which job is better if the student works less than 16.5 hours, we can set up the inequality:

1. For hours worked \( h < 16.5 \):

   • We want to know when \( 20h > 18h + 33 \): \[ 20h > 18h + 33 \]

2. Simplifying this gives: \[ 20h - 18h > 33 \] \[ 2h > 33 \] \[ h > 16.5 \]

This means that if the student works more than 16.5 hours, the restaurant job is better; conversely, if they work fewer hours, they would earn more at the hotel job.

Conclusion

• If the student works more than 16.5 hours: Restaurant job is preferable.
• If the student works less than 16.5 hours: Hotel job is preferable.

Summary

Let's put this into bullet points for clarity:

1. Hotel job pays better with fewer hours (less than 16.5).
2. Restaurant job pays better with more hours (more than 16.5).
3. Exact break-even point is at 16.5 hours.
4. Based on work preference and schedule flexibility, the student should choose accordingly.