SOLUTION: This mixture problem has me stuck. The problem: A hospital needs a 50% dextrose solution. Only a 75% and 40% solution are in stock. How much of the 75% solution should be mixed wit

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Question 993766: This mixture problem has me stuck. The problem: A hospital needs a 50% dextrose solution. Only a 75% and 40% solution are in stock. How much of the 75% solution should be mixed with 500 oz of the 40% solution to get a 50% dextrose solution. My teacher showed us how to set up the chart with the percentages and how to multiply across and add down but the column where the variables is confusing me.

Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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: 

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






Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
This mixture problem has me stuck. The problem: A hospital needs a 50% dextrose solution. Only a 75% and 40% solution are in stock. How much of the 75% solution should be mixed with 500 oz of the 40% solution to get a 50% dextrose solution. My teacher showed us how to set up the chart with the percentages and how to multiply across and add down but the column where the variables is confusing me.
Yes, the chart is good, but I’ll do the problem without it



Let the amount of 75% solution to be mixed, be S

Then amount of 75% solution in the resulting mixture = .75S

Amount of 40% solution to be mixed: 500 oz

Then amount of 40% solution in the resulting mixture = .4(500)

Equation for the resulting mixture is: .75S + .4(500) = .5(S + 500)

.75S + 200 = .5S + 250

.75S - .5S = 250 – 200

.25S = 50

S, or amount of 75% solution to mix = 50%2F.25, or highlight_green%28200%29 oz