In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. Marian consumes 510 calories by drinking 3 servings of milk and 1 soda. Using matrices to solve, how many calories are in 1 serving of milk?

Let J, M, and S represent the calories in one serving of juice, milk, and soda. Subtract Marian’s equation, 3M + S = 510, from Joe’s equation, J + 2M + S = 530, to get J − M = 20. Using that relationship in Darius’s equation, 2J + M = 370, gives 2(M + 20) + M = 370, so 3M = 330 and M = 110. One serving of milk has 110 calories, choice C.

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