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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 \$20\%\$ alcohol. The solution in the tank is thoroughly mixed. This procedure is repeated twice more. What percentage of the final solution is alcohol? Express your answer to the nearest whole number.

Dec 2, 2018

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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 \$20\%\$ alcohol. The solution in the tank is thoroughly mixed. This procedure is repeated twice more. What percentage of the final solution is alcohol? Express your answer to the nearest whole number.

After 25 gallons are drained, 75 gallons remain

So  75 *.5 + 25* .20  =  100 gallons of 42.5% alcohol

After 25 gallons of this are drained again we have

75*.425 +  25 *.20 =  100 gallons of 36.875% alcohol

After the proceedure is done for the last time

75 * .36875 + 25*.20 = 100 gallons of 32.65625% alcohol

So..... 33%   (rounded)   Dec 3, 2018