To help pay for his tuition, a college student plans to work in the evenings and on weekends. He has been offered two part-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 pay $7.50 an hour plus tips. The entire waitstaff typically collects about $50 in tips each hour. Tips are divided equally among the 4 waitstaff members who share a shift.
1.The equation  7.50h+504h=18h+33
  represents a possible constraint about a situation.

a. Solve the equation and check your solution.

Type your answer in the box.

h=
  


To solve the equation given:

\[
7.50h + 50 \cdot \frac{1}{4} h = 18h + 33
\]

1. First, simplify the terms. Since the waitstaff share the $50 tips equally, each person receives $ 50 \div 4 = 12.5 $ dollars per hour in tips. Thus, the equation becomes:

\[
7.50h + 12.5h = 18h + 33
\]

2. Combine like terms on the left side:

\[
20h = 18h + 33
\]

3. Move the $18h$ term to the left side by subtracting $18h$ from both sides:

\[
2h = 33
\]

4. Divide both sides by 2 to solve for $h$:

\[
h = \frac{33}{2} = 16.5
\]

### Solution
\[
h = 16.5
\]

### Verification
Let's substitute $h = 16.5$ back into the original equation to verify.

1. Left side:

\[
7.50(16.5) + 12.5(16.5) = 123.75 + 206.25 = 330
\]

2. Right side:

\[
18(16.5) + 33 = 297 + 33 = 330
\]

Both sides are equal, confirming that the solution is correct.

### Final Answer
\[
h = 16.5
\]

Would you like more details, or do you have any questions?

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**Related Questions:**
1. What would happen if the transportation allowance increased?
2. How does a change in the hourly tip rate affect the equation?
3. How many hours would he need to work if the restaurant tips were halved?
4. What if the hotel increased its hourly pay to $20—how would that change the equation?
5. If another job offer paid $15/hour with no allowance, how would it compare?

**Tip:** Always double-check each term in an equation, especially when multiple sources of income or expenses are combined.

To help pay for his tuition, a college student plans to work in the evenings and on weekends. He has been offered two part-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 waitstaff members who share a shift. The equation 7.50h + 504h = 18h + 33 represents a possible constraint about a situation. a. Solve the equation and check your solution. Type your answer in the box. h=

Explore the solution to the equation 7.50h + 12.5h = 18h + 33, used to compare job earnings for a college student considering two part-time job offers. This page breaks down the algebraic steps and provides a clear understanding of the concepts involved. Suitable for students in Grades 9-11.

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