SOLUTION: A 20% concentrate is to be mixed with a mixture having a concentration of 60% to obtain 80 liters of a mixture with a concentration of 30%.  How much of the 20% concentrate and the

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Question 909062: A 20% concentrate is to be mixed with a mixture having a concentration of 60% to obtain 80 liters of a mixture with a concentration of 30%.  How much of the 20% concentrate and the 60% concentrate will be needed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 20% mixture needed
+.2a+ = liters of the concentrate in 20% mixture
Let +b+ = liters of 60% mixture needed
+.6b+ = liters of the concentrate in 60% mixture
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(1) +a+%2B+b+=+80+
(2) +%28+.2a+%2B+.6b+%29+%2F+80+=+.3+
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(2) +.2a+%2B+.6b+=+24+
(2) +2a+%2B+6b+=+240+
(2) +a+%2B+3b+=+120+
Subtract (1) from (2)
(2) +a+%2B+3b+=+120+
(1) +-a+-+b+=+-80+
+2b+=+40+
+b+=+20+
and
(1) +a+%2B+b+=+80+
(1) +a+%2B+20+=+80+
(1) +a+=+60+
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60 liters of 20% mixture is needed
20 liters of 60% mixture is needed
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check:
(2) +%28+.2a+%2B+.6b+%29+%2F+80+=+.3+
(2) +%28+.2%2A60+%2B+.6%2A20+%29+%2F+80+=+.3+
(2) +%28+12+%2B+12+%29+%2F+80+=+.3+
(2) +24+=+.3%2A80+
(2) +24+=+24+
OK