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?

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