# Roselle has 2 cups of popcorn and 8 oz of soda for a total of 216 calories. Carmel has 1 cup of popcorn and 12 02 of soda for a total of 204 calories.

Roselle has 2 cups of popcorn and 8 oz of soda for a total of 216 calories. Carmel has 1 cup of popcorn and 12 02 of soda for a total of 204 calories. Determine the number of calories per cup of popcorn and per ounce of soda.

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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.