Solve the problem

Question

Most nutritionists now agree that a healthy adult diet should include 25-35g of the fiber each day. A breakfast of 2 bluberry muffins, 1 banana, and a 1-cup serving of cereal contains 16g of fiber; a breakfast of 1 blueberry muffin, 2 bananas, and a 1-cup serving of cereal contains 16.5g of fiber; and a breakfast of 2 blueberry muffins and a 1-cup serving of cereal contains 12g of fiber. How much fiber is in each of these foods?

A blueberry muffin contains

____

g of fiber

Answer 1

first, we can use variables to represent each food item, therefore:

Blue berry muffin: m

Banana: b

Cereal: c

Since all units are in grams, we don't have to convert any units...yay!

Ok, now let's rewrite the question in terms of variables:

2 bluberry muffins, 1 banana, and a 1-cup serving of cereal contains 16g of fiber

2m + b + c=16

1 blueberry muffin, 2 bananas, and a 1-cup serving of cereal contains 16.5g of fiber

m+ 2b + c=16.5

2 blueberry muffins and a 1-cup serving of cereal contains 12g of fiber

2m + c=12

Let's first solve the equation with the fewest variables:

2m+c =12

from this we get that: c= 12-2m ; we can substitute this into one of the other equations

2m +b + c = 16

2m + b + (12-2m) = 16

b + 12 = 16

b=4

Now that we know teh value of b, let's substitute this into another equation:

m + 2b + c =16.5

m + 2(4) + c =16.5

m + 8 + c = 16.5

let's now substitute for c, so that we have only one variable:

m + 8 + (12-2m) = 16.5

20 - m = 16.5

m = 3.5

Now that we have the value of m, let's find the value of c:

2m + c = 12

2(3.5) + c = 12

7 + c = 12

c = 5

therefore:

b=4, c=5, m =3.5

Solution:

bananas: 4g of fiber/serving

cereal: 5 g of fiber/ serving

blueberry muffins: 3.5 g of fiber/serving