The nutritional content per ounce of three foods

Question

The nutritional content per ounce of three foods is presented in the table on the right. If a meal consisting of the three foods allows exactly 2200 ​calories, 65 grams of​ protein, and 4550

Calories

Protein

​(in grams)

Vitamin C

​(in milligrams)

Food A 100, 7, 250

Food B 400, 7, 1050

Food C 500, 9, 150

how many ounces of each kind of food should be​ used?

Food​ A:

Food B:

Food C:

Answer 1

The system of three linear equations to solve for A, B, C:

100A + 400B + 500C = 2200

7A + 7B + 9C = 65

250A + 1050B + 150C = 4550

There are several techniques available for solving that system. If using addition/elimination then perhaps each equation should be simplified as much as possible. For example, every term of 1st equation is divisible by 100 and every term of of 3rd equation is divisible by 50.

A + 4B + 5C = 22

7A + 7B + 9C = 65

5A + 21B + 3C = 91

Perhaps you know how to use REF or RREF on your graphing calculator?

Or simply choose to for example eliminate "A" from equations 1 &3 and from 1&2, resulting in 2 equations and 2 unknowns.