document.write( "Question 989451: A number of two digits is equal to 6 times the sum of the digits, and the number formed by reversing the digits exceeds 4 times the sum of the digits by 9. What is the original number? \n" ); document.write( "

Algebra.Com's Answer #609822 by htmentor(1343) $\"\"$ $\"About$

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The original two digit number can be written as 10t + u where t = the tens digit and u = the ones digit
\n" ); document.write( "The first equation gives
\n" ); document.write( "10t + u = 6(t + u) [The number is 6 times the sum of the digits]
\n" ); document.write( "The second equation gives
\n" ); document.write( "10u + t = 4(t + u) + 9 [Reversing the digits equals the sum of the digits + 9]
\n" ); document.write( "We have two equations and two unknowns.
\n" ); document.write( "Solving for t in terms of u in the first equation gives t = (5/4)u
\n" ); document.write( "The 2nd equation gives t = 2u - 3
\n" ); document.write( "This gives u = 4, t = 5
\n" ); document.write( "Ans: 54
\n" ); document.write( "Check: 6*(5+4) = 54 \n" ); document.write( "

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