SOLUTION: A butcher has some hamburger that is 18% fat and some that is 15% fat. How many pounds of each should be mixed to make 87 lb of hamburger that is 16% fat?

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Question 831074: A butcher has some hamburger that is 18% fat and some that is 15% fat. How many pounds of each should be mixed to make 87 lb of hamburger that is 16% fat?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = pounds of meat with 18% fat needed
Let b = pounds of meat with 15% fat needed
---------------------------------
(1) +a+%2B+b+=+87+
(2) +%28+.18a+%2B+.15b+%29+%2F+87+=+.16+
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(2) +.18a+%2B+.15b+=+.16%2A87+
(2) +.18a+%2B+.15b+=+13.92+
(2) +18a+%2B+15b+=+1392+
Multiply both sides of (1) by 15 and
subtract (1) from (2)
(2) +18a+%2B+15b+=+1392+
(1) +-15a+-+15b+=+-1305+
+3a+=+87+
+a+=+29+
and, since
(1) +a+%2B+b+=+87+
(1) +29+%2B+b+=+87+
(1) +b+=+58+
29 pounds of meat with 18% fat are needed
58 pounds of meat with 15% fat are needed
check:
(2) +%28+.18%2A29+%2B+.15%2A58+%29+%2F+87+=+.16+
(2) +%28+5.22+%2B+8.7+%29+%2F+87+=+.16+
(2) +13.92+=+.16%2A87+
(2) +13.92+=+13.92+
OK