SOLUTION: Hi, I have tried this problem 2 different ways and I am still not getting correct answers. Can you show me the correct format. Find how many quarts of 6% butterfat milk and

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Question 879396: Hi,
I have tried this problem 2 different ways and I am still not getting correct answers. Can you show me the correct format.
Find how many quarts of 6% butterfat milk and 3% butterfat milk should be mixed to yield 45 quarts of 4% butterfat milk?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = quarts of 6% milk needed
Let +b+ = quarts of 3% milk needed
----------------------------------
(1) +a+%2B+b++=+45+
(2) +%28+.06a+%2B+.03b+%29+%2F+45+=+.04+
------------------------------
(2) +.06a+%2B+.03b+=+1.8+
(2) +6a+%2B+3b+=+180+
Multiply both sids of (1) by +3+
and subtract (1) from (2)
(2) +6a+%2B+3b+=+180+
(1) +-3a+-+3b+=+-135+
+3a+=+45+
+a+=+15+
and, since
(1) +a+%2B+b++=+45+
(1) +b+=+45+-+15+
(1) +b+=+30+
---------------
15 quarts of 6% milk are needed
30 quarts of 3% milk are needed
----------------------------
check:
(2) +%28+.06a+%2B+.03b+%29+%2F+45+=+.04+
(2) +%28+.06%2A15+%2B+.03%2A30+%29+%2F+45+=+.04+
(2) +%28+.9+%2B+.9+%29+%2F+45+=+.04+
(2) +1.8+=+.04%2A45+
(2) +1.8+=+1.8+
OK