Question

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?
90
110
130
180

Answer 1

Let j = juice, m = milk, s = soda. Equations:
j + 2m + s = 530
2j + m = 370
3m + s = 510

From 2nd, j = (370 − m)/2. From 3rd, s = 510 − 3m. Plug into 1st:
(370 − m)/2 + 2m + (510 − 3m) = 530 → multiply by 2:
370 − m + 4m + 1020 − 6m = 1060 → −3m + 1390 = 1060 → 3m = 330 → m = 110.

Answer: 110.