The table on the right shows the calories, sodium, and protein in one cup of var

Question

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 Calories of soup should be mixed together to produce Sodium (mg) 10 servings of soup, each of which provides 178 calories, 912 milligrams of sodium, and 11.4 grams of protein? What is the serving Chicken NoodleChicken & RiceChicken Rotini 130 510 100 490 110 690 Protein (gl size (in cups)? Toproduce 10 se Rotin gs of soup, each of which pro des 178cal es, 912magan s of sodum, and 114ga sofprotem, mxcups of Chicken Node,Cups "Chicken & Rice ar d cups ofCwke The sening size is cups (Round to the nearest tenth as needed ) Enter your answer in each of the answer boxes

Explanation / Answer

We are to produce 10 servings of soup such that each serving provides178 calories, 912 milligrams of sodium and 11.4 grams of protein;
Let number of cups of chicken noodle, chicken and rice, and chicken rotini cups required be x,y and z respectively;
100x + 130y + 110 z = 178*10 = 1780;
490x + 510y + 690z = 912*10 = 9120;
7x+ 9y + 6z = 11.4*10 = 114;  

These are 3 equations and 3 unknowns x,y,z;
Solving them we get: x=6, y=4 and z=6;
Total cups = x+y+z = 6+4+6 = 16 cups;

Thus, number of cups of chicken noodles = 6
number of cups of chicken and rice =4
number of cups of chicken rotini = 6

The serving size = total size (in cups) / number of servings = 16/10 = 1.6 cups;


Feel free to ask for any clarifications.

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