SOLUTION: Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 123 g protein, 110 g fat, and 168 g carbohydrate. According to the

Algebra ->  Equations -> SOLUTION: Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 123 g protein, 110 g fat, and 168 g carbohydrate. According to the       Log On


   

Question 1115264: Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit
his food intake to 123 g protein, 110 g fat, and 168 g carbohydrate. According to the health
conscious hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g
carbohydrate; the spicy meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate; and the
deviled eggs have 13 g protein, 15 g fat, and 6 g carbohydrate. How many of each snack
can he eat to obtain his goal?
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the number of the marinated mushroom caps;
    y be the number of the spicy meatball;
    z be the number of the deviled eggs.

According to the condition, these tree balance equations are in place:

   3x + 14y + 13z = 123  grams of protein         (1)
   5x +  7y + 15z = 110  grams of fat             (2)
   9x + 15y +  6z = 168  grams of carbohydrate    (3)


So, what Ron must do is to input the coefficients of the matrix and the right side terms into his calculator and then press the button highlight%28SOLVE%29.

Then he will obtain the answer.


Instead of calculator, I used this popular free of charge online solver in this site

https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver

written by our colleague  Jim Thompson to get this answer:


x = 9   (marinated mushroom caps),
y = 5   (spicy meatball),
z = 2   (deviled eggs).