A restaurant has one type of milk that has 2% fat and another that has 7% fat. How many quarts of each type does the restaurant need to make 40 quarts of a milk mixture that is 5% fat?

There is two milk with a different fat concentration in this question. First, you need to know the ratio of 2%:7% that will result in 5%. The equation for the fat content would be:

fat content1 + fat content2 = fat content3

2% * v1 + 7%*v2 = 5% * (v1+v2)

2*v1 + 7*v2 = 5*v1 + 5*v2

2*v1 + 7*v2 - (5*v1 + 5*v2)

-3*v1 + 2*v2=0

2*v2 = 3v1

v1:v2 = 3/2

Then for 40 quarts,

the number of 2% needed would be:

3 / (3+2) * 40 quarts = 24 quarts

the number of 7% needed would be:

2 / (3+2) * 40 quarts = 16 quarts