SOLUTION: A chemist has two solutions of sulfuric acid. The first is one half sulfuric acid and half water. The second is three-fourths sulfuric acid and one fourths water. He wishes to make

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Question 158985: A chemist has two solutions of sulfuric acid. The first is one half sulfuric acid and half water. The second is three-fourths sulfuric acid and one fourths water. He wishes to make 10 liters of a solution which is two-thirds sulfuric acid and one-thirds water. How many liters of each available solution should he use?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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: A chemist has two solutions of sulfuric acid. The first is one half sulfuric acid and half water. The second is three-fourths sulfuric acid and one fourths water. He wishes to make 10 liters of a solution which is two-thirds sulfuric acid and one-thirds water.
How many liters of each available solution should he use?
;
Let x = amt of 1%2F2 sulfuric acid solution
then
(10-x) = amt of 3%2F4 solution
:
Write an equation based on the amt of sulfuric acid
1%2F2(x) + 3%2F4(10-x) = 2%2F3(10)
Multiply equation by 12 to get rid of the denominators
6x + 9(10-x) = 8(10)
:
6x + 90 - 9x = 80
:
6x - 9x = 80 - 90
-3x = -10
x = %28-10%29%2F%28-3%29
x = + 31%2F3 liters of the 1%2F2 sulfuric acid solution
and
10 - 31%2F3 = 62%2F3 liters of 3%2F4 sulfuric acid solution
;
:
Check solution using calc:
.50(3.33) + .75(6.67) = .67(10)
1.665 + 5.00 = 6.7
6.665 ~ 6.7