document.write( "Question 612808: a two digit number is 5 times the sum of its digits and is also equal to 5 more than the product of its digit find the number
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Algebra.Com's Answer #385729 by Theo(13342) $\"\"$ $\"About$

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the number, as far as i can tell, is 50.
\n" ); document.write( "the first digit is 5.
\n" ); document.write( "the second digit is 0.
\n" ); document.write( "it can't be 05 because that's a one digit number of 5.
\n" ); document.write( "when the most significant digit is 5 and the least significant digit is 0, you get:
\n" ); document.write( "5+0=5
\n" ); document.write( "5*0+5=5
\n" ); document.write( "the sum of the digits is equal to the product of the digits plus 5.
\n" ); document.write( "the equation is generated and solved for as follows:
\n" ); document.write( "let x equal 1 of the digits and y equal the other digit.
\n" ); document.write( "you get:
\n" ); document.write( "xy+5=x+y
\n" ); document.write( "subtract x and subtract 5 from both sides of this equation to get:
\n" ); document.write( "xy-x=y-5
\n" ); document.write( "factor out the x on the left side of the equation to get:
\n" ); document.write( "x(y-1) = (y-5)
\n" ); document.write( "divide both sides of the equation by (y-1) to get:
\n" ); document.write( "x = (y-5)/(y-1)
\n" ); document.write( "since x or y have to be single digits from 0 to 9, it's then a matter of substituting a single digit from 0 to 9 for y and seeing what the value of x becomes.
\n" ); document.write( "you get:
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document.write( "y         x\r\n" );
document.write( "0         5\r\n" );
document.write( "1         undefined\r\n" );
document.write( "2         -3\r\n" );
document.write( "3         -1\r\n" );
document.write( "4         -.3333...\r\n" );
document.write( "5         0\r\n" );
document.write( "6         .2\r\n" );
document.write( "7         .3333...\r\n" );
document.write( "8         .42857...\r\n" );
document.write( "9         .5\r\n" );
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\n" ); document.write( "you can see that the only digits that come out to be intergers in the interval of from 0 to 9 are when x = 0 and y = 5 or when x = 5 and y = 0.
\n" ); document.write( "if x is the most significant digit, then the solution is x = 5 and y = 0.
\n" ); document.write( "if x is the least significant digit, then the solution is x = 0 and y = 5.\r
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