Question

you are having a party and want to estimate how much youll have to spend on pizza. each pizza costs $10. you estimate each person will eat 5 slices. a pizza is sliced into 8 slices. you are inviting 24 people.
set up the dimensional analysis problem below correctly.
empty boxes for setup = empty box
options: 1 pizza, $10, 10 pizzas, $1, 1 person, 24 persons (people), 8 slices, 10 slices, 1 slice, 5 slices, 5 people (persons), 1, 10, 5, 8, 15, $15, $150, $75, $80, $72

Explanation:

Step1: Determine total slices needed

We have 24 people, each eating 5 slices. So total slices = \(24 \text{ persons} \times \frac{5 \text{ slices}}{1 \text{ person}}\)

Step2: Determine number of pizzas needed

Each pizza has 8 slices, so number of pizzas = \(\frac{24 \times 5 \text{ slices}}{8 \text{ slices per pizza}}\)

Step3: Determine total cost

Each pizza costs \$10, so total cost = \(\frac{24 \times 5}{8} \text{ pizzas} \times \frac{\$10}{1 \text{ pizza}}\)

Putting it all together in dimensional analysis:
\(24 \text{ persons} \times \frac{5 \text{ slices}}{1 \text{ person}} \times \frac{1 \text{ pizza}}{8 \text{ slices}} \times \frac{\$10}{1 \text{ pizza}}\)

Breaking down the boxes (from top to bottom, left to right for numerator and denominator):

First box (numerator 1): 24 persons (people)
Second box (numerator 2): 5 slices
Third box (numerator 3): 1 pizza
Fourth box (numerator 4): \$10

First box (denominator 1): 1 person
Second box (denominator 2): 8 slices
Third box (denominator 3): 1 pizza
Fourth box (denominator 4): 1 (since the last fraction's denominator is 1 pizza, but we already accounted for pizza in numerator 3, actually the correct denominators are 1 person, 8 slices, 1 pizza (but the last fraction is \$10 per 1 pizza, so denominator for the last fraction is 1 pizza). Wait, maybe better to list the factors:

The dimensional analysis setup is:

\(24 \text{ persons} \times \frac{5 \text{ slices}}{1 \text{ person}} \times \frac{1 \text{ pizza}}{8 \text{ slices}} \times \frac{\$10}{1 \text{ pizza}}\)

So the boxes (top row: numerators, bottom row: denominators):

Top row (left to right): 24 persons (people), 5 slices, 1 pizza, \$10

Bottom row (left to right): 1 person, 8 slices, 1 pizza, 1 (since the last fraction is \$10 / 1 pizza, so denominator is 1 pizza, but we can write 1 for the last denominator as the units cancel:

Calculating the value:

First, \(24 \times 5 = 120\) slices needed.

Then, \(120 \div 8 = 15\) pizzas needed.

Then, \(15 \times 10 = \$150\) total cost.

So the final box (result) is \$150.

Answer:

Top row (numerators): 24 persons (people), 5 slices, 1 pizza, \$10
Bottom row (denominators): 1 person, 8 slices, 1 pizza, 1
Result box: \$150