Question

a school cafeteria has $\frac{9}{2}$ pounds of trail mix.
each student serving uses $\frac{3}{4}$ pound of trail mix.
after serving students, $\frac{1}{2}$ pound of trail mix must be set aside for a staff meeting.
how many full student servings can be made?

Explanation:

Step1: Calculate usable mix for students

Subtract staff reserve from total mix:
$\frac{9}{2} - \frac{1}{2} = \frac{8}{2} = 4$ pounds

Step2: Divide by per-serving size

Divide usable mix by $\frac{3}{4}$ per serving:
$4 \div \frac{3}{4} = 4 \times \frac{4}{3} = \frac{16}{3} \approx 5.33$

Step3: Take whole number of servings

Only full servings count, so round down.

Answer:

5 full student servings