document.write( "Question 1197844: Two alcohol solutions consists of a 35 gallons of 35% alcohol and other solutions containing 50% alcohol. If the two solutions are combined together, they will have a mixture of 40% alcohol. How many gallons of the solutions containing 50% alcohol? \n" ); document.write( "

Algebra.Com's Answer #831286 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Here are two variations of a method that can be used to solve any 2-part \"mixture\" problem like this without formal algebra.

\n" ); document.write( "(1) The 40% of the mixture is 5% away from the 35% of one ingredient and 10% away from the 50% of the other ingredient. So 40% is \"twice as close\" to 35% as it is to 50%. That means the amount of the 35% solution must be twice the amount of the 50% solution. Since there are 35 gallons of the 35% solution, there must be 35/2 = 17.5 gallons of the 50% solution.

\n" ); document.write( "ANSWER: 17.5 gallons of the 50% alcohol

\n" ); document.write( "(2) Look at the three percentages on a number line -- 35, 40, and 50 -- and observe/calculate that 40 is one-third of the way from 35 to 50. That means 1/3 of the mixture is the ingredient with the higher percentage. So the 35 gallons of 35% alcohol is 2/3 of the total; that means the 1/3 of the total that is the 50% alcohol is half of 35 gallons, which is 17.5 gallons.

\n" ); document.write( "ANSWER: 17.5 gallons of the 50% alcohol

\n" ); document.write( "CHECK:
\n" ); document.write( ".35(35)+.50(17.5) = 12.25+8.75 = 21
\n" ); document.write( ".40(35+17.5) = .40(52.5) = 21

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