Question

Natalie kept track of her calcium intake from three sources for 3 days. The first day she had 2 glasses of milk, 4 servings of ice cream, and 3 calcium supplements in pill form which totaled 2600 mg of calcium. The second day she had 3 glasses of milk, 4 servings of ice cream, and 3 calcium supplements totaling 3200 mg. The third day she had 2 glasses of milk, 5 servings of ice cream, and 3 calcium supplements for a total of 2650 mg. Find the amount of calcium in one glass of milk, in one serving of ice cream, and in one calcium supplement.

Answer 1

Let the amounts of calcium in milk, ice cream and supplements be
x, y, and z respectively

2x + 4y + 3z = 2600
3x + 4y + 3z = 3200
2x + 5y + 3z = 2650

easy to solve:
subtract #1 from #2 ---> x = 600
subtract #2 from #3 ---> -x + y = -550
plug in x = 600
-600 + y = -550 ---> y = 50
back into the first:
2x + 4y + 3z = 2600
1200 + 200 + 3z = 2600

finish it up