word problem algebra

Question

most nutritionists now agree that a healthy diet should include 25-35 g of fiber each day. A breakfast of 2 blueberry muffins, 1 banana, and a 1-cup serving of cereal contains 10 g fiber. A breakfast of 1 blueberry muffin, 3 bananas, and a 1-cup serving of cereal contains 16.5 g of fiber and a breakfast of 2 blueberry muffins and a 1-cup serving of cereal contains 6 g of fiber. how much fiber is in each of these foods?

Answer 1

Hi Jakob F

Did you notice that you have a given substitution that you can use?

If you write your equations directly as given you have an immediate substitution you can use to solve for B

Let M = muffins

Let B = Bananas

Let C = Cereal

Equation 1

2M + B + C = 10

Equation 2

M + 3B + C = 16.5

Equation 3

2M + C = 6

Equation 1 and Equation 3 both contain 2M + C which is 6

If you substitute 6 for 2M + C you can easily and quickly find B

B = 10 - 6 = 4

Plug in 4 for B in Equation 2 you will have another equation in M and C

M + 3B + C = 16.5

M + 3(4) + C = 16.5

M +12 + C = 16.5

M + C + 16.5 - 12

M + C = 4.5

Subtract M + C = 4.5 from 2M + C = 6 to solve for M

2M + C = 6

-(M + C = 4.5)

Gives

2M + C = 6

-M - C = -4.5

M = 1.5

You can use the information above to solve for C and check by plugging all the values back into the original equations. Of course it should agree with the elimination method used above as well.

Answer 2

2M +B + C = 10

multiply by 3

6M+3B +3C =30

subtract to eliminate B

M + 3B + C = 16.5

5M +2C = 13.5

2M + C = 6

4M +2C = 12

M = 1.5

C = 6-2M = 6-2(1.5) = 3

B =10 -2M-C = 10-3-3 = 4

Muffins have 1.5 grams, Cereal 3 grams, Bananas 4 grams