document.write( "Question 1049169: A two-digit number is such that the sum of its digit is 1/8 of the number.
\n" ); document.write( "When the digits of the number are reversed and the number is subtracted from the original number, the result obtained is 45. Find the original number please. \n" ); document.write( "

Algebra.Com's Answer #664776 by MathTherapy(10552) $\"\"$ $\"About$

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\n" ); document.write( "A two-digit number is such that the sum of its digit is 1/8 of the number.
\n" ); document.write( "When the digits of the number are reversed and the number is subtracted from the original number, the result obtained is 45. Find the original number please.
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Let the tens and units digits of the original number be T, and U, respectively
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document.write( "Then number is: 10T + U, and when reversed, it becomes: 10U + T
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document.write( "Then: 
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document.write( "10T + U = 8(T + U) ------ Cross-multiplying
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document.write( "10T + U = 8T + 8U
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document.write( "10T - 8T = 8U - U
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document.write( "2T = 7U ------- eq (i)\r
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document.write( "Also, 10T + U - (10U + T) = 45
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document.write( "10T + U - 10U - T = 45 =====> 9T - 9U = 45 ======> 9(T - U) = 9(5) ======> T - U = 5 ======> T = 5 + U ------ eq (ii)
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document.write( "2(5 + U)  = 7U ------ Substituting 5 + U for T in eq (i)
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document.write( "10 + 2U = 7U
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document.write( "10 = 7U - 2U
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document.write( "10 = 5U
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document.write( "U, or units digit of original number =  = 2\r
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document.write( "T = 5 + 2 ------- Substituting 2 for U in eq (ii)
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document.write( "T, or tens digit of original number = 7\r
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document.write( "Original number:  \n" );
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