How much salt must be added to 800 grams of a solution that is 15% to obtain a solution that is 20% salt?

Question

5980 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-24T20:43:08

You would add 50 g of salt.

We will assume that the density of the solution remains constant (even though the density changes with concentration!).

A 15 % concentration means

$15 % = "15 g salt"/"100 g solution"$

So the mass of salt in 800 g of solution is

$"Mass of salt" = 800 color(red)(cancel(color(black)("g soln"))) × "15 g salt"/(100 color(red)(cancel(color(black)("g soln")))) = "120 g salt"$

So you have $"120 g salt"/"800 g soln"$ .

You want to add $x " g of salt"$ to get a 20 % solution.

This also increases the mass of the solution by $x " g"$ .

Then

$(120 + x)/(800+x) = 20/100$

$100(120+x)=20(800+x)$

$12000+100x= 16000+20x$

$80x = 5000$

$x=50$

You would have to add 50 g of salt.

Check:

$(120+50)/(800+50) = 20/100$

$170/850 = 20/100$

$1/5 = 1/5$

It checks!