document.write( "Question 1163645: The sum of two whole numbers is 45 and their difference is less than 10. The numbers of all possible pairs is? \n" ); document.write( "

Algebra.Com's Answer #787804 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "What do you need help with...?

\n" ); document.write( "Make a list of all pairs of whole numbers with a sum of 45 and identify the pairs in which the difference is less than 10.

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document.write( "  44  1\r\n" );
document.write( "  43  2\r\n" );
document.write( "  42  3\r\n" );
document.write( "  41  4\r\n" );
document.write( " ...\r\n" );
document.write( "  30 15\r\n" );
document.write( "  29 16\r\n" );
document.write( "  28 17\r\n" );
document.write( "  27 18\r\n" );
document.write( "  26 19\r\n" );
document.write( "  25 20\r\n" );
document.write( "  24 21\r\n" );
document.write( "  23 22

\n" ); document.write( "The problem doesn't talk about ORDERED pairs, so I am assuming the pair 22 and 23 is the same as the pair 23 and 22; so you can stop there.

\n" ); document.write( "It is easy to see that there are 5 pairs of numbers that satisfy the given condition.

\n" ); document.write( "ANSWER: 5 pairs

\n" ); document.write( "Here is a solution using logical reasoning and a few simple mental calculations to find the answer, without writing out all those pairs.

\n" ); document.write( "(1) The sum of two whole numbers is 45; that means one of them is odd and one is even.
\n" ); document.write( "(2) That means the difference between the two numbers is odd.
\n" ); document.write( "(3) The difference has to be less than 10; there are 5 positive odd integers less than 10.

\n" ); document.write( "ANSWER: 5 pairs

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