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 common cereals are given below. Suppose a mixture of these two cereals is to be prepared that contains exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat. a. Set up a vector equation for this problem. Include a statement of what the variables in your equation represent. b. Write an equivalent matrix equation, and then determine if the desired mixture of the two cereals can be prepared.

Complete Question:

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 common cereals are given below. Suppose a mixture of these two cereals is to be prepared that contains exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat. a. Set up a vector equation for this problem. Include a statement of what the variables in your equation represent. b. Write an equivalent matrix equation, and then determine if the desired mixture of the two cereals can be prepared.

Nutrient         General mills cheerios        Quaker 100% Natural cereal

Calories                       110                                           130

Protein (g)                    4                                                3

Carbohydrate (g)         20                                             18

Fat (g)                           2                                                 5

Solution:

Representation of data in equation.

x1 is the number of servings of Cheerios and

x2 is the number of servings of Natural Cereal

110 + 130  = 295

4 + 3 = 9

20 + 18 = 48

2 + 5 = 8

Representation of data in vector equation,

  +  =

Equivalent matrix equation of data

Row reduce the matrix

 ≅

1.5 serving of cherrios with 1 serving of natural cereal requried to make desired mixture.

= 1.5 , = 1

a) +  =  

b) = 1.5 , = 1

B. Solution

Explanation:

According to the question statement, Susan wrote in her notebook that it was a blue liquid. Therefore, from a chemistry point of view, it was a solution and not a heterogeneous mixture. Then, the solvent was evaporated after leaving the solution for 72 hours at the windowsill. The solute (blue color most likely) however was not able to evaporate with solvent and left behind.

Example: if you leave the KMnO4+water solution for a few days, water will evaporate thus leaving behind purple crystals of KMnO4.