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.