document.write( "Question 1194289: The ages of two sisters are 9 and 12 years respectively. In how many years time will the product of their ages be 418 years? \n" ); document.write( "

Algebra.Com's Answer #826450 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "The response from the other tutor shows a perfectly good formal algebraic solution -- which is probably what you were looking for.

\n" ); document.write( "But you can get some very good mental exercise by solving the problem using logical reasoning. Here is one way to do that.

\n" ); document.write( "(1) Their ages are not far apart. So think of them as \"about the same\", so that the product of their ages will be close to a perfect square.
\n" ); document.write( "(2) Then look for a perfect square that is close to 418. 400 = 20^2 is close. So the two ages 10 years from now will be two whole numbers close to 20 whose product is 418 and whose difference is 3.
\n" ); document.write( "(3) The last digit of the product is 8; two numbers with a difference of 3 and close to 20 which multiplied together give last digit 8 are 19 and 22.

\n" ); document.write( "Then multiplying 22*19 shows that those are the correct ages 10 years from now, so their current ages are 9 and 12.

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