What mass of a 10 % solution must I add to a 20 % solution to get 500 g of a 17.5 % solution?

1 Answer
Ernest Z.
Jan 19, 2017

You must add 125 g of the 10 % solution to 375 g of the 20 % solution.

Explanation:

Let the mass of the 10 % solution be xcolor(white)(l)"g".

Then the mass of the 20 % solution is (500 - x)color(white)(l) "g".

We have the relation

"mass of solute in 10 % solution" + "mass of solute in 20 % solution" = "mass of solute in 17.5 % solution"

x color(red)(cancel(color(black)("g"))) × 10 color(red)(cancel(color(black)(%))) + (500 - x) color(red)(cancel(color(black)("g"))) × 20 color(red)(cancel(color(black)(%))) = 500 color(red)(cancel(color(black)("g"))) × 17.5 color(red)(cancel(color(black)(%)))

10x + 20(500 - x) = 500 × 17.5

10x + "10 000" - 20x = 8750

10 x = 1250

x = 1250/10 = 125

You must add 125 g of the 10 % solution to 375 g of the 20 % solution.

Check:

"125 g"× 10 % + "375 g" × 10 % = "500 g" × 17.5 %

"12.5 g + 37.5 g = 50 g"

"50 g = 50 g"

It checks!

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