document.write( "Question 1183595: The sum of the two whole numbers is 45 and their difference is less than 10. The number of all possible pairs is??? \n" ); document.write( "

Algebra.Com's Answer #813993 by greenestamps(13215) $\"\"$ $\"About$

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\n" ); document.write( "Logically, if the sum of two whole numbers is 45, then one of them is even and the other is odd.

\n" ); document.write( "If two whole numbers are one even and the other odd, then their difference is an odd number.

\n" ); document.write( "Since the problem requires that the difference between the two numbers be less than 10, the difference can be either 1, 3, 5, 7, or 9.

\n" ); document.write( "So there are 5 pairs of whole numbers that satisfy the conditions of the problem.

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

\n" ); document.write( "Algebraically....

\n" ); document.write( "Let the larger number be x and the smaller be y.

\n" ); document.write( " $\"x%2By=45\"$
\n" ); document.write( " $\"x-y%3C10\"$

\n" ); document.write( "Solve the first equation for y:
\n" ); document.write( " $\"y=45-x\"$

\n" ); document.write( "Substitute in the inequality:
\n" ); document.write( " $\"x-%2845-x%29%3C10\"$
\n" ); document.write( " $\"2x-45%3C10\"$
\n" ); document.write( " $\"2x%3C55\"$
\n" ); document.write( " $\"x%3C27.5\"$

\n" ); document.write( "The larger number has to be less than 27.5, so the largest it can be is 27.

\n" ); document.write( "That's as far as the algebraic solution gets you; you still have to do some logical reasoning to find the answer to the problem.

\n" ); document.write( "Since x is the larger of the two numbers, it has to be greater than 45/2=22.5, so the smallest it can be is 23.

\n" ); document.write( "That means the larger number can be any whole number between 23 and 27, inclusive; that is 5 numbers.

\n" ); document.write( " \n" ); document.write( "

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