For another picnic, you want to make hamburgers with pickles, again without havi

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.

Explanation / Answer

Solution:-

In chemical symbolism, you're looking to balance:
B8 + H12 + P18 BHP3
Start by finding the lowest common multiple of 8 and 12, which is 24.
So start with a total of 24 buns and 24 hamburger patties:
3 B8 + 2 H12 + P18 24 BHP3
Now you've got 72 pickles on the right, so you need 72, taken 18 at a time, on the left:
3 B8 + 2 H12 + 4 P18 24 BHP3
Now the equation is balanced and there is no common factor of the four coefficients, so to make 24 hamburgers you need 3 packages of buns, 2 packages of hamburger patties and 4 jars of pickles.

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