SOLUTION: a candy company wants to mix a 10% fat content chocolate with a 60% fat cantent chocolate to obtain 50 pounds of a 30% fat content chocolate. how many pounds of each kind of chocol

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Question 583681: a candy company wants to mix a 10% fat content chocolate with a 60% fat cantent chocolate to obtain 50 pounds of a 30% fat content chocolate. how many pounds of each kind of chocolate must be used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of 10% fat chocolate needed
Let +a+ = pounds of 60% fat chocolate needed
given:
+.1a+ = pounds of fat in 10% chocolate
+.6b+ = pounds of fat in 60% chocolate
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(1) +a+%2B+b+=+50+
(2) +%28+.1a+%2B+.6b+%29+%2F+50+=+.3+
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(2) +.1a+%2B+.6b+=+.3%2A50+
(2) +.1a+%2B+.6b+=+15+
(2) +a+%2B+6b+=+150+
Subtract (1) from (2)
(2) +a+%2B+6b+=+150+
(1) +-a+-+b+=+-50+
+5b+=+100+
+b+=+20+
and, since
(1) +a+%2B+b+=+50+
(1) +a+%2B+20+=+50+
(1) +a+=+30+
30 pounds of 10% fat chocolate is needed
20 pounds of 60% fat chocolate is needed
check:
(2) +%28+.1%2A30+%2B+.6%2A20+%29+%2F+50+=+.3+
(2) +%28+3+%2B+12+%29+%2F+50+=+.3+
(2) +15%2F50+=+.3+
(2) +15+=+15+
OK