SOLUTION: 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% butter

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Question 1019724: 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? (Hint: there are 4 quarts in a gallon)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Convert gallons to quarts:
+2%2A4+=+8+ quarts
Let +x+ = quarts of milk should be
drained and replaced by pure butterfat
-------------------------------
+.02x+ = pure butter fat in +x+
quarts of milk
--------------------------------
+.02%2A8+=+.16+ = original quarts of butterfat
----------------
Note that you start with 8 quarts and
end up with 8 quarts
+%28+.16+-+.02x+%2B+x+%29+%2F+8+=+.05%0D%0A%7B%7B%7B+%28+.16+%2B+.98x+%29+%2F+8+=+.05+
+.16+%2B+.98x+=+.4+
+.98x+=+.24+
+x+=+.2449+
.2449 quarts of milk must be drained and
replaced with pure butterfat
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check:
+.02%2A.2449+=+.004898+ quarts of
butterfat is drained off
----------------------
+.2449+ quarts of butterfat is added
----------------------------------
+%28+.16+-+.004898+%2B+.2449+%29+%2F+8+=+.05+
+.4%2F8+=+.05+
+.4+=+.4+
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Strange numbers -definitely get a 2nd opinion
-unless the answer is already known.