SOLUTION: A chemist 80 mil of 25% chemical solution. he only has a 50% chemical solution and a 10% chemical solution. find how many ml of each he should mix to get the desired solution.

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A chemist 80 mil of 25% chemical solution. he only has a 50% chemical solution and a 10% chemical solution. find how many ml of each he should mix to get the desired solution.       Log On


   



Question 659460: A chemist 80 mil of 25% chemical solution. he only has a 50% chemical solution and a 10% chemical solution. find how many ml of each he should mix to get the desired solution.
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 50% solution needed
Let +b+ = ml of 10% solution needed
given:
(1) +a+%2B+b+=+80+
(2) +%28+.5a+%2B+.1b+%29+%2F+80+=+.25+
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(2) +.5a+%2B+.1b+=+.25%2A80+
(2) +.5a+%2B+.1b+=+20+
(2) +5a+%2B+b+=+200+
Subtract (1) from (2)
(2) +5a+%2B+b+=+200+
(1) +-a+-+b+=+-80+
+4a+=+120+
+a+=+30+
and, since
(1) +a+%2B+b+=+80+
(1) +30+%2B+b+=+80+
(1) +b+=+50+
30 ml of 50% solution are needed
50 ml of 10% solution are needed
check:
(2) +%28+.5%2A30+%2B+.1%2A50+%29+%2F+80+=+.25+
(2) +%28+15+%2B+5+%29+%2F+80+=+.25+
(2) +20+=+.25%2A80+
(2) +20+=+20+
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A chemist 80 mil of 25% chemical solution. he only has a 50% chemical solution and a 10% chemical
-------
Equation:
active + active = active
0.50x + 0.10(80-x) = 0.25*80
----
Multiply thru by 100 to get:
50x + 10*80 - 10x = 25*80
40x = 15*80
x = 30 ml (amt. of 50% solution needed)
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80-x = 70 ml (amt. of 10% solution needed)
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Cheers,
Stan H.