document.write( "Question 933311: The sum of the digits of a two digit number is 9. The number is twice the product of its digits. Find the number. \n" ); document.write( "

Algebra.Com's Answer #566739 by stanbon(75887) $\"\"$ $\"About$

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The sum of the digits of a two digit number is 9. The number is twice the product of its digits. Find the number.
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\n" ); document.write( "Let the number be 10t+u
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\n" ); document.write( "Equations:
\n" ); document.write( "t + u = 9
\n" ); document.write( "10t+u = 2tu
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\n" ); document.write( "Substitute for \"t\" and solve for \"u\":
\n" ); document.write( "10(9-u) + u = 2(9-u)u
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\n" ); document.write( "90 - 9u = 18u - 2u^2
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\n" ); document.write( "2u^2 - 27u + 90 = 0
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\n" ); document.write( "(2u-15)(u-6) = 0
\n" ); document.write( "u = 7.5 (extraneous because the answeer must be a whole number)
\n" ); document.write( "u = 6
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\n" ); document.write( "Solve for \"t\":
\n" ); document.write( "t + u = 9
\n" ); document.write( "t + 6 = 9
\n" ); document.write( "t = 3
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\n" ); document.write( "Ans: 10t+u = 36
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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