Question

consider a picnic. if you want to buy enough hot dogs and buns 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 hot dogs (which usually contain 10 dogs). what is the smallest number of packages of buns and hot dogs you need, respectively? express your answer as two integers separated by a comma. view available hint(s) packages submit part b complete previous part(s) part c 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)

Explanation:

Step1: Find LCM of 8 and 10

Prime factors: $8=2^3$, $10=2\times5$. LCM = $2^3\times5=40$

Step2: Calculate bun packages

Number of bun packages = $\frac{40}{8}=5$

Step3: Calculate hot dog packages

Number of hot dog packages = $\frac{40}{10}=4$

Step4: Adjust pickle count per hamburger

Each hamburger needs 3 pickles, so effective pickle per "unit": $\frac{18}{3}=6$ servings per jar

Step5: Find LCM of 8,12,6

Prime factors: $8=2^3$, $12=2^2\times3$, $6=2\times3$. LCM = $2^3\times3=24$

Step6: Calculate bun packages (Part C)

Number of bun packages = $\frac{24}{8}=3$

Step7: Calculate patty packages (Part C)

Number of patty packages = $\frac{24}{12}=2$

Step8: Calculate pickle jars (Part C)

Number of pickle jars = $\frac{24}{6}=4$

Answer:

Part A: 5, 4
Part C: 3, 2, 4