Question

Heavy cream is 36% butterfat while whole milk contains only 4% butterfat. In order to make a delicious pint of ice cream, a recipe calls for 2 cups of a mixture that is 24% butterfat. How many cups of heavy cream should be used to produce the correct butterfat percentage?

Answer 1

`1(1)/(4)\text{ or }1.25` cups of heavy cream.

Explanation:

Let x represent cups of heavy cream and y represent cups of whole milk.

We have been given that a recipe calls for 2 cups of a mixture. We can represent this information in an equation as:

`x+y=2...(1)`

We are also told that heavy cream is 36% butterfat, so butterfat in x cups of heavy cream would be
`0.36x`.

We are also told that whole milk contains only 4% butterfat, so butterfat in y cups of whole milk would be
`0.04y`.

The recipe calls for 2 cups of a mixture that is 24% butterfat. We can represent this information in an equation as:

`0.36x+0.04y=2(0.24)...(2)`

From equation (1), we will get:

`y=2-x`

Upon substituting this value in equation (2), we will get:

`0.36x+0.04(2-x)=2(0.24)`

`0.36x+0.08-0.04x=0.48`

Combine like terms:

`0.32x+0.08=0.48`

`0.32x+0.08-0.08=0.48-0.08`

`0.32x=0.40`

`(0.32x)/(0.32)=(0.40)/(0.32)`

`x=(40)/(32)`

`x=(5)/(4)`

`x=1(1)/(4)`

`x=1.25`

Therefore,
`1(1)/(4)\text{ or }1.25` cups of heavy cream should be used to produce the correct butterfat percentage.