SOLUTION: Nicole started a new diet that requires each meal to have 280 calories, 4 grams of fiber, and 6 g of fat. The table shows the fiber, fat, and calorie content of one serving of each

Question 1120365: Nicole started a new diet that requires each meal to have 280 calories, 4 grams of fiber, and 6 g of fat. The table shows the fiber, fat, and calorie content of one serving of each of three breakfast foods. How many servings of each food should Nicole eat to follow her diet?
toast
serving(s)
cottage cheese
serving(s)
fruit
serving(s)
Food Fiber (g) Fat (g) Calories
Toast 2 1 100
Cottage cheese 0 5 120
Fruit 2 0 60

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Let x be the number of servings of toast, y the number of servings of cottage cheese, and z the number of servings of fruit. With the given data, the three equations are

(1) fiber: 2x+0y+2z = 4, or x+y = 2
(2) fat: x+5y+0z = 6, or x+5y = 6
(3) calories: 100x+120y+60z = 280, or 5x+6y+3z = 14

Solving this system is almost trivial. Comparing the first two equations gives us y = 1; then either of the first two gives us x = 1; then the third gives us z = 1.

Answer: 1 serving of each
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