SOLUTION: I understand what the question is asking me. My problem is I do not know how to set it up to solve it. If I could just figure out how it write the formula I could probably solve it

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Question 399944: I understand what the question is asking me. My problem is I do not know how to set it up to solve it. If I could just figure out how it write the formula I could probably solve it. It goes as follows:
How much 2% alcohol must be mixed with 10% alcohol to get 2000 ml of 8% alcohol?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = ml of 2% alcohol needed
Let b = ml of 10% alcohol needed
It follows, then:
.02a = ml of alcohol in 2% solution
.1b = ml of alcohol in 10% solution
In words:
(ml of alcohol in final solution)/(ml of solution) = 8%
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(1) %28.02a+%2B+.1b%29%2F2000+=+.08
(2) a+%2B+b+=+2000
----------------
(1) .02a+%2B+.1b+=+160
(1) 2a+%2B+10b+=+16000
Multiply both sides of (2) by 2
and subtract (2) from (1)
(1) 2a+%2B+10b+=+16000
(2) -2a+-+2b+=+-4000
8b+=+12000
b+=+1500 ml
And,
a+%2B+b+=+2000
a+=+2000+-+1500
a+=+500 ml
500 ml of 2% alcohol are needed
1500 ml of 10% alcohol are needed
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check answer:
(1) %28.02a+%2B+.1b%29%2F2000+=+.08
(1) %28.02%2A500+%2B+.1%2A1500%29%2F2000+=+.08
(1) %2810+%2B+150%29%2F2000+=+.08
160%2F2000+=+.08
160+=+160
OK