SOLUTION: A candy company wants to produce 20 kilograms of a special 45% fat content chocolate. To obtain this, a 50% fat content chocolate is combined with a 30% fat content chocolate. How

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Question 739702: A candy company wants to produce 20 kilograms of a special 45% fat content chocolate. To obtain this, a 50% fat content chocolate is combined with a 30% fat content chocolate. How many kilograms of the 50% fat content and the 30% fat content are used to make the required 20 kilograms?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = kg of 50% fat chocolate needed
Let +b+ = kg of 30% fat chocolate needed
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(1) +a+%2B+b+=+20+ kg
(2) +%28+.5a+%2B+.3b+%29+%2F+20+=+.45+
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(2) +.5a+%2B+.3b+=+.45%2A20+
(2) +.5a+%2B+.3b+=+9+
(2) +5a+%2B+3b+=+90+
Multiply both sides of (1) by +3+
and subtract (1) from (2)
(2) +5a+%2B+3b+=+90+
(1) +-3a+-+3b+=+-60+
+2a+=+30+
+a+=+15+
and, since
(1) +a+%2B+b+=+20+
(1) +b+=+5+
15 kg of 50% fat chocolate are needed
5 kg of 30% fat chocolate are needed
check:
(2) +%28+.5a+%2B+.3b+%29+%2F+20+=+.45+
(2) +%28+.5%2A15+%2B+.3%2A5+%29+%2F+20+=+.45+
You can check