How much heavy cream and low-fat milk should you combine in order to obtain 2 cups of half and half?

Question

You need half and half (with a fat content of 13%), but you only have heavy cream (with a fat content of 37%) and low-fat milk (with a fat content of 1%).  How much heavy cream and low-fat milk should you combine in order to obtain 2 cups of half and half? 

 

Define, in words, any variable you introduce. Include units, when appropriate. You must use equations to solve the problem. Guess and check answers will not receive full credit. 

Answer 1

Looking at the fat concentrations.

We have x cups of 37% fat heavy cream = 0.37x cups of fat

To this we add (2-x) cups of 1% low fat milk = 0.01(2-x) cups of fat

These total to 2 cups of 13% fat half and half = 0.13(2) cups of fat

 

0.37x + 0.01(2-x) = 0.13(2)

Clear decimals by multiplying through by 100

37x + (2-x) = 13(2)

36x + 2 = 26

36x = 24

x = 24/36 = 2/3 cups heavy cream

2-x = 2 - 2/3 = 1 1/3 cups of low fat milk

 

We combine 2/3 cups of heavy cream to 1 1/3 cups of low fat milk

to obtain 2 cups of half and half