document.write( "Question 1162996: You need a 20% acid solution. You have 980 mL of 15% on hand. How much of a 90% acid solution should you add to obtain the desired solution? \n" ); document.write( "

Algebra.Com's Answer #786935 by greenestamps(13206) $\"\"$ $\"About$

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\n" ); document.write( "Here is an alternative to the standard algebraic solution method shown by the other tutor.

\n" ); document.write( "The 20% target is much closer to the 15% of the original solution than it is to the 90% of the solution that is being added. So the amount of 90% acid being added should be very small compared to the 980mL of the original solution.

\n" ); document.write( "Specifically, 20% is only 1/15 of the way from 15% to 90%. (15 to 90 is a difference of 75; 15 to 20 is a difference of 5; 5/75 = 1/15.)

\n" ); document.write( "That means 1/15 of the final mixture should be the 90% acid that is being added.

\n" ); document.write( "So the 980mL of the original 15% acid is 14/15 of the final mixture; that makes 1/15 of the final mixture 980/14 = 70mL.

\n" ); document.write( "ANSWER: 70mL of the 90% acid should be used.

\n" ); document.write( "CHECK:
\n" ); document.write( ".15(980)+.90(70) = 147+63 = 210
\n" ); document.write( ".20(980+70) = .20(1050) = 210

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