A tank holds 100 gallons of a thoroughly mixed solution which is 50% alcohol. Twenty-five gallons are drained from the tank and replaced with a solution that is \(40\%\) alchohol. The solution in the tank is thoroughly mixed. This procedure is repeated 2 more times. What percentage of the final solution is alcohol? Express your answer to the nearest whole number.

 May 14, 2022

You can repeat my calculations 2 more times on your own, but here's how to do the first replacement of solutions:


After 25 gallons are drained, there are 75 gallons of solution with 50% alcohol. That means half of them is alcohol and half of them is other things. So we have 37.5 gallons of alcohol in the tank if you multiply 50% by 75 gallons. 


Now we pour the 25 gallons of 40% alcohol into the tank. That is actually 25(40%) = 10 gallons of extra alcohol and 25 gallons of extra total solution, so we have 100 gallons of solutions again, but the new concentration of alcohol is \(\dfrac{37.5 + 10}{100} \times 100\% = 47.5\%\) instead.


Can you repeat this process twice on your own? If you didn't understand the method, you can ask under this comment.

 May 14, 2022

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