Solve Problems Using Systems in Three Variables
-Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 127 g protein, 110 g fat, and 147 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?
A) 6 mushrooms; 5 meatballs; 3 eggs
B) 5 mushrooms; 3 meatballs; 6 eggs
C) 3 mushrooms; 6 meatballs; 5 eggs
D) 7 mushrooms; 6 meatballs; 4 eggs

Question

Quizplus · Accepted Answer

To solve this problem, set up a system of equations based on the given information. Let x represent the number of mushroom caps, y the number of spicy meatballs, and z the number of deviled eggs. The equations based on protein, fat, and carbohydrate content respectively are:3x + 14y + 13z = 127 (Protein)5x + 7y + 15z = 110 (Fat)9x + 15y + 6z = 147 (Carbohydrate)Solving this system of equations yields the solution x = 6, y = 5, and z = 3, which corresponds to choice A: 6 mushrooms, 5 meatballs, 3 eggs.