SOLUTION: If 1,600 liters of 10% dextrose solution is made by combining a 20% dextrose solution with a 4% dextrose solution, how much of each solution must be used

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Question 1077533: If 1,600 liters of 10% dextrose solution is made by combining a 20% dextrose solution with a 4% dextrose solution, how much of each solution must be used
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 20% solution needed
Let +b+ = liters of 4% solution needed
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(1) +a+%2B+b+=+1600+
(2) +%28+.2a+%2B+.04b+%29+%2F+1600+=+.1+
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(2) +.2a+%2B+.04b+=+160+
(2) +20a+%2B+4b+=+16000+
(2) +5a+%2B+b+=+4000+
Subtract (1) from (2)
(2) +5a+%2B+b+=+4000+
(1) +-a+-+b+=+-1600+
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+4a+=+2400+%7B%7B%7B%0D%0A%7B%7B%7B+a+=+600+
and
(1) +a+%2B+b+=+1600+
(1) +600+%2B+b+=+1600+
(1) +b+=+1000+
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600 liters of 20% solution are needed
1000 liters of 4% solution are needed
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check:
(2) +%28+.2a+%2B+.04b+%29+%2F+1600+=+.1+
(2) +%28+.2%2A600+%2B+.04%2A1000+%29+%2F+1600+=+.1+
(2) +%28+120+%2B+40+%29+%2F+1600+=+.1+
(2) +160+%2F+1600+=+.1+
(2) +160+=+160+
OK