SOLUTION: A butcher has some hamburger that is 21% fat and some that is 15% fat. How many pounds of each should be mixed to make 75 lb of hamburger that is 17% fat?

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Question 704562: A butcher has some hamburger that is 21% fat and some that is 15% fat. How many pounds of each should be mixed to make 75 lb of hamburger that is 17% fat?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of 21% hamburger needed
Let +b+ = pound of 15% hamburger needed
given:
(1) +a+%2B+b+=+75+
(2) +%28+.21a+%2B+.15b+%29+%2F+75+=+.17+
-----------------------------
(2) +.21a+%2B+.15b+=+.17%2A75+
(2) +.21a+%2B+.15b+=+12.75+
(2) +21a+%2B+15b+=+1275+
Multiply both sides of (1) by +15+ and
subtract (1) from (2)
(2) +21a+%2B+15b+=+1275+
(1 ) +-15a+-+15b+=+-1125+
+6a+=+150+
+a+=+25+
and
(1) +25+%2B+b+=+75+
(1) +b+=+50+
25 pounds of 21% hamburger are needed
50 pound of 15% hamburger are needed
check:
(2) +%28+.21%2A25+%2B+.15%2A50+%29+%2F+75+=+.17+
(2) +%28+5.25+%2B+7.5+%29+%2F+75+=+.17+
(2) +12.75+%2F+75+=+.17+
(2) +12.75+=+.17%2A75+
(2) +12.75+=+12.75+
OK