SOLUTION: I was told to get a second opinion on this question - Two gallons of milk contain 2% butterfat. How many quarts of milk should be drained and replaced by pure butterfat to prod

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Question 1019921: I was told to get a second opinion on this question -
Two gallons of milk contain 2% butterfat. How many quarts of milk should be drained and replaced by pure butterfat to produce a mixture of two gallons of milk containing 5% butterfat? (4 quarts in a gallon)
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
We have 2 gallons or 2*4 = 8 quarts of mixture
Let x be the number of quarts to replace with 100% fat to produce 5% mixture
(2%(8-x) + 100%(x) )/8 equals 5/100
That is 2% times the amount left after removing x quarts plus
100% times the same x quarts now being replaced
divided by 8, since we will continue to have 8 quarts.
This is set equal to 5/100 or 5%
%280.02%288-x%29+%2B+1%28x%29+%29%2F8+=+5%2F100
%280.16-0.02x+%2B+x+%29%2F8+=+5%2F100
%280.16%2B0.98x+%29%2F8+=+5%2F100
100%280.16%2B0.98x+%29+=+8%2A5
100%280.16%2B0.98x+%29+=+40
16%2B98x++=+40
add -16 to each side
98x++=+24
Divide each side by 98
x = 24/98
x = 0.2449 quarts
Double check
Substitute 0.2449 for x in %280.02%288-x%29+%2B+1%28x%29+%29%2F8
%280.02%288-0.2449%29+%2B+1%280.2449%29+%29%2F8
%280.02%287.7551%29+%2B+0.2449+%29%2F8
%280.400002+%29%2F8
0.05000025
5.000025% , so we have it