Question 993766
sometimes those charts are helpful.


i'm not sure how helpful they are here.


the basic problem is this.


you have two solutions.
we'll call them A and B.


A is a 40% solution
B is a 75% solution


C is the new solution that you want that is a 50% solution.


you have 500 ounces of the 40% solution.
you have x ounces of the 75% solution.
you will have 500 + x ounces of the 50% solution.


your equation will be:


.40 * 500 + .75 * x = .50 * (500 + x)


you need to solve for x.


simplify the equation to get:


200 + .75 * x = 250 + .50 * x


subtract .50 * x from both sides of the equation and subtract 200 from both sides of the equation to get:


.75 * x - .50 * x = 250 - 200


combine like terms to get:


.25 * x = 50


divide both sides of this equation by .25 to get:


x = 50 / .25 = 200


go back to your original equation of .40 * 500 + .75 * x = .50 * (500 + x) and replace x with 200 to get:


.40 * 500 + .75 * 200 = .50 * (500 + 200)


simplify this equation to get:


200 + 150 = 250 + 100


combine like terms on each side of this equation to get:


350 = 350.


this confirms the value of x is equal to 200 to be good.


i had difficulty fitting a chart to this problem.


best i could come up with it this:


<pre>
mix                      A             B            C
total ounces             500           x            x + 500
persent solution         40%           75%          50%
ounces solution          .4 * 500      .75 * x      .50 * (x + 500)
</pre>