74.5% alcohol solution, when added into a certain amount of 54.5% alcohol solution, form 280 litres of 59.5% alcohol. How many litres of 74.5% alcohol were there at first?

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Let a litres be the amount of the stronger alcohol solution, then 280-a litres of the other solution are mixed with it to produce 280L altogether. The amounts of pure alcohol mixed are represented by:

0.745a+0.545(280-a)=0.595×280=166.6, meaning that the final solution contains 166.6L of pure alcohol.

So, 0.745a+152.6-0.545a=166.6, 0.2a=166.6-152.6=14, a=14/0.2=70L.

So initially there was 70L of 74.5% alcohol solution.

by Top Rated User (766k points)

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