SOLUTION: How many quarts of a pure solution must be added to a 5% solution to get 4 quarts of a 14.5% solution? Find equation(s) and solve. Not out of text book!

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Question 52591: How many quarts of a pure solution must be added to a 5% solution to get 4 quarts of a 14.5% solution?
Find equation(s) and solve.
Not out of text book!
Answer by ankor@dixie-net.com(12684) About Me  (Show Source):
You can put this solution on YOUR website!
How many quarts of a pure solution must be added to a 5% solution to get 4 quarts of a 14.5% solution?
Convert the decimal to % solutions:
:
We know that the amounts of the the two solutions add up 4 qt
:
Let x = amt of pure solution
Pure solution is 1.00(x)
:
Therefore the 5% solution amt is: .05[4-x]
:
The resulting solution: .145(4)
The equation: .05[4-x] + 1.00[x] = .145(4)
:
Mult, get rid of the brackets:
.2 - .05x + 1x = .58
1x - .05x = .58 - .2
.95x = .38
x = .38/.95
x = .4 qts of pure solution must be added
:
:
Check by substitution: 5% amt = 4 - .4 = 3.6 qts
:
.05(3.6) + .4 = .145[4)
.18 + .4 = .58 proves our value for x