The question in the book was "What percentage of a $35\%$ solution of alcohol in water should be replaced by pure alcohol to give a solution containing 75% alcohol? Assume that the original solution contains 100 units."
Here's how I answered it: $35\%(100) + 100\%(x) = 75\%(100 + x)$
after solving, I got $x = 160$ and then I tried to express 100 as a percentage of 160 which resulted to $61 + \frac{7}{13}\%$ which is the correct answer. But the answer was a complete guess so my question is, how do I go think about or rather, how do I visualize "what percentage should be replaced" so that I could answer similar problems in the future.
Thanks!