document.write( "Question 1154729: Gabe Amodeo, a nuclear physicist, needs 60liters of a 40% acid solution. He currently has a 30 % solution and a 60 % solution. How many liters of each does he need to make the needed 6060 liters of 40% acid solution? \n" ); document.write( "

Algebra.Com's Answer #777214 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "You should know how to solve problems like this using a formal algebraic method, such as the one shown by the other tutor.

\n" ); document.write( "If an algebraic solution is not required, here is a fast and easy way to solve two-part mixture problems like this:

\n" ); document.write( "(1) The target 40% is \"twice as close\" to 30% as it is to 60%.
\n" ); document.write( "(2) Therefore, the mixture must contain twice as much of the 30% ingredient as the 60% ingredient.

\n" ); document.write( "Twice as much of the 30% as the 60%, and a total of 60 liters, means 40 liters of the 30% acid solution and 20 liters of the 60% acid solution.

\n" ); document.write( "ANSWER: 40 liters of the 30% acid; 20 liters of the 60% acid.

\n" ); document.write( "Here is another way to look at the same solution method.

\n" ); document.write( "Think of starting with 30% acid and adding 60% acid until the mixture is 40% acid.

\n" ); document.write( "You started at 30% and moved towards 60%, stopping when you reached 40%.

\n" ); document.write( "40% is one-third of the way from 30% to 60%.

\n" ); document.write( "Therefore, 1/3 of the mixture is the 60% acid you are adding.

\n" ); document.write( "ANSWER: 1/3 of 60 liters, or 20 liters, of the 60% acid solution; the other 40 liters are the 30% solution.

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