Question

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

Answer 1

You would add 50 g of salt.

Explanation:

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!