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

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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!