Word problem

Question

Most nutritionists now agree that a healthy adult diet should include 25minus35 g of fiber each day. A breakfast of 2 blueberry muffins, 1 orange, and a 1-cup serving of cereal contains 14 g of fiber; a breakfast of 1 blueberry muffin, 3 oranges, and a 1-cup serving of cereal contains 19.5 g of fiber; and a breakfast of 2 blueberry muffins and a 1-cup serving of cereal contains 10 g of fiber. How much fiber is in each of these foods?
A blueberry muffin contains
nothing g of fiber.

Answer 1

To solve this problem, you would need to use systems of equations. There are many ways to solve this. This is how I solved it.

B = Blueberr

O = Orange

C = Cereal

Now put the word problems into equation:

2B + O + C = 14

B + 3O + C = 19.5

2B + C = 10

Because the first and last equation only differ by an orange, I subtracted the last equation from the first as follows:

2B + O + C = 14

-(2B + C = 10)

C = 4 This means that the orange has 4 grams of fiber.

Now we will have to 1.) solve for one of the variable, 2.) substitute it into another equation and solve for the other variable, and 3.) substitute that variable into original equation. This is as follows:

1.) B + 3O + C = 19.5 Substitute in 4 for orange(O)

B + 3(4) + C = 19.5 Solve for B

B + 12 + C = 19.5

B + C = 7.5

B= 7.5 - C

2.) 2B + C = 10 Substitute the value for B into this equation and solve for C

2( 7.5 - C) + C = 10

15 - 2C + C = 10

-C = -5

C = 5

3.) B= 7.5 - C Substitute the value of C into the first equation.

B= 7.5 - 5

B = 2.5

Now, we have the fiber content of all of the foods.

Orange has 4 grams of fiber

Cereal has 5 grams of fiber

Blueberries have 2.5 grams of fiber.