SOLUTION: One ounce of each of three foods has the vitamin and mineral content shown in the table. How many ounces of each must be used to provide exactly 21 milligrams (mg) of niacin, 11 m

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Question 906778: One ounce of each of three foods has the vitamin and mineral content shown in the table. How many ounces of each must be used to provide exactly 21 milligrams (mg) of niacin, 11 mg of zinc, and 17 mg of vitamin C?
Food A----- oz
Food B------ oz
Food C ------ oz
Food Niacin Zinc Vitamin C
A 1 mg 1 mg 2 mg
B 2 mg 1 mg 1 mg
C 2 mg 1 mg 2 mg
(mg stands for milligram)
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Let a, b, c, be the amount of ounces of each of the foods. Form equations this way: r%5B1%5D%2Aa%2Br%5B2%5D%2Ab%2Br%5B3%5D%2Ac=v, to account for the v quantity of each specified nutrient. Each r%5Bi%5D is milligrams of nutrient per ounce of food item.


1%2Aa%2B2%2Ab%2B2%2Ac=21, accounting for the milligrams of Niacin.
1%2Aa%2B1%2Ab%2B1%2Ac=11, accounts for zinc.
2%2Aa%2B1%2Ab%2B2%2Ac=17, accounts for vitamin C.

Solve, any method you want or need. Matrices be best.