SOLUTION: HOW MANY GRAMS OF PURE SALT MUST BE ADDED TO 40 GRAMS OF A 20% SALT SOLUTION TO MAKE A SOLUTION THAT IS 36% SALT?

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Question 1844: HOW MANY GRAMS OF PURE SALT MUST BE ADDED TO 40 GRAMS OF A 20% SALT SOLUTION TO MAKE A SOLUTION THAT IS 36% SALT?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
For a 20% salt solution, one fifth (ie 20%) is salt. As we have 40g of the solution, then 8g (ie a fifth) must be salt.
we would work out the % by saying (8/40)*100 = 20%
However, we now will add some more salt. Call this unknown amount, x grams. We therefore increase the amount of salt by 8 and the total amount by 8 too. And the new salinity is 36%. So, we have %28%288%2Bx%29%2F%2840%2Bx%29%29%2A100+=+36
Re-arranging this gives
%28%288%2Bx%29%2F%2840%2Bx%29%29+=+%280.36%29
%288%2Bx%29+=+%280.36%29%2840%2Bx%29
%288%2Bx%29+=+%2814.4+%2B+%280.36%29%28x%29%29
Rearranging this again gives
%280.64%29%28x%29+=+%286.4%29
hence x=10g of salt required.
We can see this in the formula...it is now (18/50)*100 which is 36%
cheers
Jon.