Math, microeconomics

Question

Gerber Product's Gerber Mixed Cereal for Baby contains, in each serving, 60 calories and 11 grams of carbohydrates.† Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.† If you want to provide your child with 220 calories and 53 grams of carbohydrates, how many servings of each should you use?

Gerber Mixed Cereal for Baby ...... serving(s)

Gerber Mango Tropical Fruit Dessert ........ serving(s)

Answer 1

Hello Aaa A,

Let C = The number of servings of Gerber Mixed Cereal and

Let M = The number of servings of  Gerber Mango Tropical Fruit Dessert

The total calories = 60C + 80D = 220 (equation 1)

The total carbohydrates = 11C + 21D = 53 (equation 2)

There are multiple ways to solve this equation (elimination, substitution, graphing and augmented matrices)

The method demonstrated by Raymond B. is elimination. The solution by graphing is to graph the two lines and their intersection will be the solution. Augmented matrices are often not taught, but are essentially another way to perform the elimination method. Below, I will show the substitution method.

In the substitution method we select one of the equations and solve for one of the variables.

Then we plug this solution into the other equation. Which will leave us with a one variable equation to solve.

After solving equation in one variable, we plug it back into either of the two equations and solve for the second variable.

It is usually easier to work with smaller numbers. We see that a common factor in all terms of equation 1 is 20. So, simplify by dividing all terms by 20 and equation 1 becomes

3C + 4D = 11 Solving for C yields C=(11 - 4D)/3 (equation 3)

Plug this solution for C into equation 2

11C + 21D = 53

11(11-4D)/3 +21D = 53

multiply both sides by 3

11(11-4D) + 63D = 159

Distribute 11 across (11-4D)

121 - 44D + 63D = 159

Combine like terms

19D + 121 = 159

Subtract 121 from both sides

19D = 38

divide both sides by 19

D = 2

Sub into equation 3

C = (11 - 4(2) ) /3 = 3/3 = 1

There are many chances to make a simple math error when solving these simultaneous equations, So it is a good idea to check your answer by subtituting it back into the original equations.

Seeing that you are in Alg 2, you will likely be solving for 3 variables with 3 equations. And my experience is that checking your answer is even more important when solving for 3 variables.

Equation 1

60C + 80D = 220

60(1) + 80(2) = 60 +160 = 220

Equation 2

11C + 21D = 53

11 (1) + 21 (2) = 11 + 42 = 53

So our solution of C= 1 and D = 2 checks in both equations.

Hope this helps.

Best Regards,

Dean Creech

Answer 2

60B + 80D = 220

divide by 20

3B + 4D = 11

multiply by 11

33B +44D =121

11B + 21D = 53

multiply by 3

33B +44D = 121

33B +63D = 159

33B+44D = 121

subtract to eliminate one variable

19D = 38

D = 38/19 =2

3B +8 =11

3B = 3

B =1

Fruit Desert servings of 2

Baby serving of 1