SOLUTION: Cream is approximately 22% butterfat. How many gallons of cream must be mixed with milk testing at 2% butterfat to get 20 gallons of milk containing 4% butterfat?

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Question 560444: Cream is approximately 22% butterfat. How many gallons of cream must be mixed with milk testing at 2% butterfat to get 20 gallons of milk containing 4% butterfat?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = gallons of cream needed
Let +m+ = gallons of milk needed
given:
+.22c+ = gallons of butterfat in cream used
+.02m+ = gallons of butterfat in milk used
--------
(1) +c+%2B+m+=+20+
(2) +%28+.22c+%2B+.02m+%29+%2F+20+=+.04+
---------------------------
(2) +.22c+%2B+.02m+=+.04%2A20+
(2) +.22c+%2B+.02m+=+.8+
(2) +22c+%2B+2m+=+80+
(2) +11c+%2B+m+=+40+
Subtract (1) from (2)
(2) +11c+%2B+m+=+40+
(1) +-c+-+m+=+-20+
+10c+=+20+
+c+=+2+
and, since
(1) +c+%2B+m+=+20+
(1) +2+%2B+m+=+20+
(1) +m+=+18+
2 gallons of cream must be used
check answer:
(2) +%28+.22%2A2+%2B+.02%2A18+%29+%2F+20+=+.04+
(2) +%28+.44+%2B+.36+%29+%2F+20+=+.04+
(2) +.8+=+.04%2A20+
(2) +.8+=+.8+
OK