Question

for another picnic, you want to make hamburgers with pickles, again without having any left over. you need to balance the number of packages of buns (which usually contain 8 buns) with the number of packages of hamburger patties (which usually contain 12 patties) and the number of jars of pickles (which contain 18 slices). assume that each hamburger needs three pickle slices. what is the smallest number of packages of buns, packages of patties, and jars of pickles, respectively? express your answer as three integers separated by commas. view available hint(s) 3,2,4 packages previous answers correct part d in part c, you determined that the proper ratio of packages of buns, packages of patties, and jars of pickles is 3:2:4. if you want to feed at least 300 people, but also maintain the proper ratio, what minimum number of packages of buns, packages of patties, and jars of pickles do you need, respectively? express your answer as three integers separated by commas. view available hint(s)

Explanation:

Step1: Find burgers per ratio set

Each ratio set (3,2,4) gives:
Buns: $3 \times 8 = 24$ burgers
Patties: $2 \times 12 = 24$ burgers
Pickles: $\frac{4 \times 18}{3} = 24$ burgers
So 1 ratio set feeds 24 people.

Step2: Calculate number of ratio sets

Find the smallest integer $n$ where $24n \geq 300$.
$n = \lceil \frac{300}{24}
ceil = \lceil 12.5
ceil = 13$

Step3: Scale each package count

Buns: $3 \times 13 = 39$
Patties: $2 \times 13 = 26$
Pickles: $4 \times 13 = 52$

Answer:

39, 26, 52