Question 1127585: Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 114 g protein, 95 g fat, and 141 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(52787)   (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 = 114 grams of protein (1)
5x + 7y + 15z = 95 grams of fat (2)
9x + 15y + 6z = 141 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  .
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 = 6 (marinated mushroom caps),
y = 5 (spicy meatball),
z = 2 (deviled eggs).
Solved.
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