Question

2021-08-04

Let x be the number of calories per cup of popcorn and y be the number of calories per ounce of soda.

2 cups of popcorn and 8 oz of soda have a total of 216 calories:

\(\displaystyle{2}{x}+{8}{y}={216}{\left({1}\right)}\)

1 cup of popcorn and 12 oz of soda have a total of 204 calories:

\(\displaystyle{x}+{12}{y}={204}{\left({2}\right)}\)

Divide (1) by 2 to obtain (3):

\(\displaystyle{x}+{4}{y}={108}{\left({3}\right)}\)

Subtract each side of (2) and (3) to eliminate xx and solve for y:

\(\displaystyle{8}{y}={96}\)

\(\displaystyle{y}={12}\)

Solve for xx using (2):

\(\displaystyle{x}+{12}{\left({12}\right)}={204}\)

\(\displaystyle{x}+{144}={204}\)

\(\displaystyle{x}={60}\)

So, there are 60 calories per cup of popcorn and 12 calories per ounce of soda.

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