1) The container of a breakfast cereal usually lists the number of calories and the amounts of protein, carbohydrate, and fat contained in one serving of the cereal. The amounts for two cereals are given in the data table below. Suppose a mixture of these two cereals is to be prepared that contains exactly 380calories, 14g of protein, 54g of carbohydrate, and 10g of fat. Use this information to answer the questions. Nutrition Information Per Serving Nutrient Cereal A Cereal B Calories 120 130 Protein (g) Carbohydrate (g) Fat (g) 4 22 16 a) Set up a vector equation for this problem. Let X, be the number of servings for cereal A and let X2 be the number of servings for cereal B. b) Write an equivalent matrix equation. c) Determine if the desired mixture of the two cereals can be prepared. If so, state the number of servings for each cereal, A and B.
1) The container of a breakfast cereal usually lists the number of calories and the amounts of protein, carbohydrate, and fat contained in one serving of the cereal. The amounts for two cereals are given in the data table below. Suppose a mixture of these two cereals is to be prepared that contains exactly 380calories, 14g of protein, 54g of carbohydrate, and 10g of fat. Use this information to answer the questions. Nutrition Information Per Serving Nutrient Cereal A Cereal B Calories 120 130 Protein (g) Carbohydrate (g) Fat (g) 4 22 16 a) Set up a vector equation for this problem. Let X, be the number of servings for cereal A and let X2 be the number of servings for cereal B. b) Write an equivalent matrix equation. c) Determine if the desired mixture of the two cereals can be prepared. If so, state the number of servings for each cereal, A and B.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Transcribed Image Text:1) The container of a breakfast cereal usually lists the number of calories and the amounts of protein, carbohydrate,
and fat contained in one serving of the cereal. The amounts for two cereals are given in the data table below.
Suppose a mixture of these two cereals is to be prepared that contains exactly 380calories, 14g of protein, 54g
of carbohydrate, and 10g of fat. Use this information to answer the questions.
Nutrition Information Per Serving
Nutrient
Cereal A
Cereal B
Calories
120
130
Protein (g)
Carbohydrate (g)
Fat (g)
4
22
16
2
4
a) Set up a vector equation for this problem. Let X, be the number of servings for cereal A and let X2
be the number of servings for cereal B.
b) Write an equivalent matrix equation.
c) Determine if the desired mixture of the two cereals can be prepared. If so, state the number of servings for each
cereal, A and B.
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