document.write( "Question 30965: The sum of two consecutive odd integers is at most 123. Find the pair with the greatest sum. \n" ); document.write( "

Algebra.Com's Answer #17734 by josmiceli(19441) $\"\"$ $\"About$

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The sum of any two odd integers is even. That's because odd = even + 1
\n" ); document.write( "odd[1] = even[1] + 1
\n" ); document.write( "odd[2] = even[2] + 1
\n" ); document.write( "--------------------
\n" ); document.write( "odd[1] + odd[2] = even[1] + even[2] + 2
\n" ); document.write( "The right side is definitely even
\n" ); document.write( "so the sum of the two consecutive odd integers can't be 123. I'll try 122
\n" ); document.write( "An odd integer can be expressed as 2n+1. Whatever n is, 2n+1 is guaranteed to be odd
\n" ); document.write( "The next odd integer is 2n + 3
\n" ); document.write( "(2n+1) + (2n+3) = 122
\n" ); document.write( "4n + 4 = 122
\n" ); document.write( "2n + 2 = 61
\n" ); document.write( "2n = 59
\n" ); document.write( "2n + 1 = 60
\n" ); document.write( "this needs to be odd for n to be an integer, so I'll call it 59
\n" ); document.write( "The next odd integer is 61
\n" ); document.write( "59 + 61 = 120
\n" ); document.write( "I'll see if the next consectutive pair is greater than 123
\n" ); document.write( "61 + 63 = 124
\n" ); document.write( "It is greater, so the answer is 59 and 61 \n" ); document.write( "

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