document.write( "Question 164608: The product of the two-digit number and its tens digit is 54. Find the number if the sum of the digits when added to the number gives a result of 36? \n" ); document.write( "

Algebra.Com's Answer #121291 by stanbon(75887) $\"\"$ $\"About$

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The product of the two-digit number and its tens digit is 54. Find the number if the sum of the digits when added to the number gives a result of 36?
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\n" ); document.write( "Let the number be 10t+u where t is the tens digit and u is the ones digit.
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\n" ); document.write( "EQUATION:
\n" ); document.write( "t(10t+u) = 54
\n" ); document.write( "(t+u)+ 10t+u = 36
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\n" ); document.write( "Rearrange the equations:
\n" ); document.write( "10t^2 + tu = 54
\n" ); document.write( "11t + 2u = 36
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\n" ); document.write( "u = (36-11t)/2
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\n" ); document.write( "Substitute into the quadratic to get:
\n" ); document.write( "10t^2 + t[(36-11t)/2] = 54
\n" ); document.write( "20t^2 + 36t - 11t^2 = 108
\n" ); document.write( "9t^2 + 36t - 108 = 0
\n" ); document.write( "t^2 + 4t - 12 = 0
\n" ); document.write( "(t+6)(t-2) = 0
\n" ); document.write( "t = 2 (the tens digit is 2)
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\n" ); document.write( "u = (36-11*2)/2 = 7 (the units digit is 7)
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\n" ); document.write( "The number is 27
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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