# When Frank and Mark finished milking, they found that they had 900 pounds of milk that was 2% butterfat. How much butterfat did they have to add to raise the butterfat content to 10%?

Jul 3, 2018

The added butterfat weighs $191 l b s$.

#### Explanation:

The number of pounds of butterfat in the 900 pounds of milk was

2% "of " 900 lbs = 0.02*900 lbs = 18 lbs

Then we can say that there was 982 lbs of not-butterfat.

Assume we add enough butterfat that the mixture has 10% butterfat. Let the total weight of the final mixture be ${T}_{w}$. Then 90% of the mixture is the 982 lbs of not-butterfat.

As a percentage, 90% "of " T_w = 982 lbs" " another way of writing that is

$0.90 \cdot {T}_{w} = 982 l b s \text{ }$ solving for ${T}_{w}$ yields

${T}_{w} = \frac{982 l b s}{.9} = 1091 l b s$

Therefore the added butterfat must weigh $1091 l b s - 900 l b s = 191 l b s$

I hope this helps,
Steve