![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
\n" ); document.write( "Let the two page numbers be n and n+1. Note that to be page numbers in a book, the page number on the right should be odd, so n should be even and n+1 odd.
\n" ); document.write( "Algebraically, we would need to solve the equation
\n" ); document.write( "
\n" ); document.write( "However, trying to solve that algebraically would lead to having to find two numbers that differ by 1 and whose product is 3422. But that's what the original problem asked us to do -- so the formal algebra doesn't help us.
\n" ); document.write( "Instead we can find the answer by trial and error, but with logical analysis.
\n" ); document.write( "The two numbers differ by 1, so the product 3422 is close to a perfect square; a \"nice\" perfect square close to 3422 is 60^2=3600. So the two numbers n and n+1 should be just under 60.
\n" ); document.write( "And to get a product with units digit 2 by multiplying two consecutive integers that are a bit less than 60, the only possibility is 58*59. And performing that calculation confirms that the product is indeed 3422.
\n" ); document.write( "So the two page numbers are 58 and 59.
\n" ); document.write( "ANSWER: The sum of the two page numbers is 58+59=117
\n" ); document.write( " \n" ); document.write( "