Part-time work

Question

To help for his tuition, a college student plans to work in the evenings and on weekends. He has been offered two pert-time jobs: working in the guest services department at a hotel and waiting tables at a popular restaurant.
the job at the hotel pays $18 an hour and offers $33 in transportation allowance per month.
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 among the 4 wait staff members who share a shift.
The equation 7.50h+50/4h = 18h + 33 represents a possible constraint about a situations

Answer 1

To analyze the situation, let's break down the earnings from both job options and then clarify the equation given.

Job at the Hotel:

• Hourly Wage: $18
• Monthly Transportation Allowance: $33
• Total Earnings in terms of hours worked (h):
  \[ \text{Earnings} = 18h + 33 \]

Job at the Restaurant:

• Hourly Wage: $7.50
• Tips per Hour (shared among 4 waitstaff):
  • Total tips collected per hour: $50
  • Tips per waitstaff per hour: \( \frac{50}{4} = 12.50 \)
• Total Earnings in terms of hours worked (h):
  \[ \text{Earnings} = 7.50h + 12.50h = (7.50 + 12.50)h = 20h \]

Setting Up the Equation:

The equation \( 7.50h + \frac{50}{4}h = 18h + 33 \) is trying to illustrate a balance between the earnings from both jobs.

• The left side represents the earnings from the restaurant job: \[ 7.50h + 12.50h = 20h \quad \text{(Total earnings from restaurant)} \]

• The right side represents the earnings from the hotel job: \[ 18h + 33 \quad \text{(Total earnings from hotel)} \]

Thus, the correct equation for setting the two jobs' earnings equal at any hour \( h \) would be: \[ 20h = 18h + 33 \] or rearranging gives: \[ 20h - 18h = 33 \implies 2h = 33 \implies h = 16.5 \]

Conclusion:

The equation indicates that if the college student works approximately 16.5 hours, the total earnings from both jobs would be equal. For the student to choose the better option, he should consider the total hours he is willing to work and how close he can get to that point, and the overall benefits of each job, such as the work environment and schedule.