SOLUTION: How much water should be added to 1000 cu. cm. of 80% sugar solution to prepare a 35% solution?

Question 1117132: How much water should be added to 1000 cu. cm. of 80% sugar solution to prepare a 35% solution?
Found 2 solutions by addingup, greenestamps:
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
0.8(1000)+x = 0.35(1000+x)
800+x = 350+0.35x
450 = 0.65x
x = 450/0.65 = 692.31 cu cm is how much water you have to add.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The other tutor worked the wrong problem....

His initial equation says he is adding more pure sugar to an 80% sugar solution to get a 35% sugar solution; of course that isn't going to work. An error in his algebra allowed him to come up with a wrong answer.

If you are going to use his algebraic method for solving the problem, the original equation has to be

You can finish the solution of the problem by that method if you want.

When one of the ingredients being mixed is 0% one thing and 100% the other -- as in this case where you are adding 100% water and 0% sugar -- I find a different approach to the problem easier, as explained below.

The original solution of 1000 cc of 80% sugar solution contains .80(1000) = 800 cc of sugar.
When the water is added, that same 800 cc of sugar is now 35% of the solution.
So the total volume of the solution is now 800/.35 = 2285.7 cc (approximately).
So the amount of water that needs to be added is 2285.7-1000 = 1285.7 cc.
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