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%?

1 Answer
Steve J.
Jul 3, 2018

The added butterfat weighs # 191 lbs#.

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*T_w= 982 lbs" "# solving for #T_w# yields

#T_w = (982 lbs)/.9 = 1091 lbs#

Therefore the added butterfat must weigh #1091 lbs -900 lbs = 191 lbs#

I hope this helps,
Steve

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