Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intaketo 163 g protein, 147 g fat, and 195 g carbohydrate. According to the health conscious hostess, themarinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs have 14 gprotein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, and 6 gcarbohydrate. How many of each snack can he eat to obtain his goal?
A)9 mushrooms, 6 meatballs, 4 eggs
B)6 mushrooms, 4 meatballs, 9 eggs
C)4 mushrooms, 9 meatballs, 6 eggs
D)10 mushrooms, 7 meatballs, 5 eggs

Question

Quizplus · Accepted Answer

Let x be the number of marinated mushroom caps, y be the number of spicy meatballs, and z be the number of deviled eggs. Then we can set up the following system of equations:

3x + 14y + 13z = 163 (g protein)
5x + 7y + 15z = 147 (g fat)
9x + 15y + 6z = 195 (g carbohydrate)

Using matrix algebra or substitution, we can solve for x, y, and z:

x = 9
y = 6
z = 4

Therefore, Ron should eat 9 mushrooms, 6 meatballs, and 4 deviled eggs to obtain his goal. Choice A is the only option that matches this combination.

Write the Word or Phrase That Best Completes Each Statement