document.write( "Question 212196: A number of small towns set up their own telephone system. Between each pair of towns they stretched a main phone cable. In all, they put up 28 separate cables connecting all of the towns. How many towns were there? \n" ); document.write( "

Algebra.Com's Answer #161022 by rapaljer(4671) $\"\"$ $\"About$

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This is a combination problem. Let x = number of towns. \r
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\n" ); document.write( "\n" ); document.write( "Then, C(x,2) = 28. This will be $\"%28x%2A%28x-1%29%29%2F%282%2A1%29=28\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2+-x%29%2F2=28\"$
\n" ); document.write( " $\"x%5E2-x=56\"$
\n" ); document.write( " $\"x%5E2+-x+-56=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-8%29%28x%2B7%29=0\"$
\n" ); document.write( "x=8 or x= -7\r
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\n" ); document.write( "\n" ); document.write( "Reject the negative value of x, so x=8 towns!\r
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\n" ); document.write( "\n" ); document.write( "R^2\r
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