The table on the right shows the calories sodium and protein

The table on the right shows the calories, sodium, and protein in one cup of various kinds of soup. How many cups of each kind of soup should be mixed together to produce 10 servings of soup, each of which provides 161 calories, 803 milligrams of sodium, and 11.0 grams of protein? What is the serving size (in cups)? To produce 10 servings of soup, each of which provides 161 calories. 803 milligrams of sodium, and 11.0 grams of protein, mix cups of Chicken Noodle, cups of Chicken and Rice, and cups of Chicken Rotini.

Solution

Let a cups of chicken noodles, b cups of chicken and rics & c cups of chicken rotini are mixed to produce 10 servings of soup.

The serving size in cups = (a+b+c)/10

Equations for the given data are :

100 a + 130 b + 120 c = 1610 => 10 a + 13 b + 12 c = 161

520 a+ 590 b+ 610 c= 8030 => 52 a+ 59 b+ 61 c= 803

7 a+ 9 b+ 8 c= 110

Solving these by Matrix method the answer comes out to be

a = 5

b = 3

c = 6

Therefore serving size = (5 + 3 + 6)/10 = 1.5 cups/serving.