SOLUTION: What quantity of 70 per cent acid solution must be mixed with a 30 solution to produce 1080 mL of a 50 per cent solution?

Question 280774: What quantity of 70 per cent acid solution must be mixed with a 30 solution to produce 1080 mL of a 50 per cent solution?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
A key part of solving these types of problems is keeping track of how much 'pure' stuff you need.
You need 1080 mL of 50% solution = .5*1080 = 540 mL of pure acid.
.
x = volume of 70% acid you will use
y = volume of 30% acid you will use
.
BUT since you know x+y = 1080, it is better to define the volumes in terms of 'x' only
.
y = 1080-x
.
Set up an equation that will describe the two parts and the final result
.
.7x + .3(1080-x) = .5*1080
.
multiply by 10 to get rid of decimals
7x + 3(1080-x) = 5*1080 = 5400
.
expand, collect, simplify...
.
7x + 3240 - 3x = 5400
4x = 2160
x = 540
.
y = 1080 - 540 = 540
.
So our proposed solution is 540 mL of 70% acid and 540 mL of 30% solution.
By inspection that makes sense because (.7+.3)/2 = .5
But we need to check our work...always...
.
How much 'pure' acid will be in the final solution compared to how much you need.
You need 540 mL.
.
.7*540 = 378
.3*540 = 162
378 + 162 = 540
Correct!
.
Answer:
You need to mix 540 mL of 70% acid with 540 mL of 30% acid to produce 1080 mL of 50% acid.
.
Done
RELATED QUESTIONS
What quantity of 75 per cent acid solution must be mixed with a 25 per cent solution to... (answered by josmiceli)

What quantity of 70 per cent acid solution must be mixed with a 30 solution to produce... (answered by mananth)

What quantity of 75 per cent acid solution must be mixed with a 30 per cent solution to... (answered by stanbon)

What quantity of 60 per cent acid solution must be mixed with a 30 per cent solution to... (answered by modi.kk91)

What quantity of 70 per cent acid solution must be mixed with a 20 percent solution to... (answered by checkley77)

What quantity of 70 per cent acid solution must be mixed with a 15 percent solution... (answered by ankor@dixie-net.com,checkley79)

What quantity of 75 per cent acid solution must be mixed with a 30 percent solution to... (answered by checkley77)

(1 pt) What quantity of 65 per cent acid solution must be mixed with a 30 percent... (answered by josmiceli)

What quantity of 60 per cent acid solution must be mixed with a 30 solution to produce... (answered by josgarithmetic)