SOLUTION: How many liters of a 50% acid solution must be mixed with 25% acid solution to get 250 L of a 40% acid solution? And can you guide me step by step. I was a bit confused on how t

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Question 409134: How many liters of a 50% acid solution must be mixed with 25% acid solution to get 250 L of a 40% acid solution?
And can you guide me step by step. I was a bit confused on how to get the answer.
I know Mixture:amount x concentrate
and the table, but putting it all together is confusing me

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = liters of 50% solution needed
Let b = liters of 25% solution needed
given:
(1) a+%2B+b+=+250
.5a+%2B+.25b = liters of salt in final solution
-----------------
In words:
(liters of salt) / (liters of total solution) = 40%
%28.5a+%2B+.25b%29+%2F+250+=+.4
.5a+%2B+.25b+=+.4%2A250
.5a+%2B+.25b+=+100
(2) 50a+%2B+25b+=+10000
Multiply both sides of (1) by 25, and
subtract from (2)
(2) 50a+%2B+25b+=+10000
(1) -25a+-+25b+=+-6250
25a+=+3750
a+=+150
and, since
a+%2B+b+=+250
b+=+250+-+150
b+=+100
150 liters of 50% solution and 100 liters of 25% solution are needed
check answer:
%28.5a+%2B+.25b%29+%2F+250+=+.4
%28.5%2A150+%2B+.25%2A100%29+%2F+250+=+.4
%2875+%2B+25%29%2F250+=+.4
100+=+.4%2A250
100+=+100
OK