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have a 700ml solution of 30% acid, needs a 50% solution of acid. How many ml of 100% acid should be added?

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hmmm ok. so we're saying that the entire solution needs to be .5 (50%)
so you can solve an equation like this: (.3*700 + 1*x)/(x+700) = .5
so multiplying both sides by x+700, we get : .5x + 350 = x + 210

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subtract .5 from both sides, and you get .5x + 210 = 350
so .5x = 140
140/.5 = x = 280
so I'd say 280ml
basically - .5 is the entire fraction of acid in the total solution, hence my equation in the first step - so we know the first part of the end solution since it's given
700ml * .3 is pure acid
what you add to the solution, is also pure 100% acid, so 1*x
the denominator in this case will be the total amount of solution (so the original 700ml plus whatever you added)
and we know that the entire thing - the fraction - is .5
and following that logic the answer is 280ml
i.e. .5 = total ml acid / total ml solution (after you've added everything)
good luck!
Thank you

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