SOLUTION: How much milk (3% butterfat content) was mixed with cream (27% butterfat) to produce 26 cups of Half-and-Half (11% butterfat content)? Let X be the amount of milk and Y be the amou

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Question 1024364: How much milk (3% butterfat content) was mixed with cream (27% butterfat) to produce 26 cups of Half-and-Half (11% butterfat content)? Let X be the amount of milk and Y be the amount of cream.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = cups of milk needed
Let +y+ = cups of cream needed
-----------------------------
(1) +x+%2B+y+=+26+
(2) +%28+.03x+%2B+.27y+%29+%2F+26+=+.11+
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(2) +.03x+%2B+.27y+=+2.86+
(2) +3x+%2B+27y+=+286+
Multiply both sides of (1) by +3+
and subtract (1) from (2)
(2) +3x+%2B+27y+=+286+
(1) +-3x+-+3y+=+-+78+
----------------------
+24y+=+208+
+y+=+8.667+
and
(1) +x+%2B+y+=+26+
(1) +x+=+17.333+
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17 and 1/3 cups of milk are needed
8 and 2/3 cups of cream are needed
---------------
check:
(2) +%28+.03x+%2B+.27y+%29+%2F+26+=+.11+
(2) +%28+.03%2A17.333+%2B+.27%2A8.667+%29+%2F+26+=+.11+
(2) +%28+.52+%2B+2.34+%29+%2F+26+=+.11+
(2) +2.86+%2F+26+=+.11+
(2) +2.86+=+2.86+
OK