document.write( "Question 68859: The value of a certain 2 digit number is 5 times the sum of its digits. If the digits are reversed,the resulting number 9 more than the original number . Find the original number. T is supposed to represent the tens, and U is supposed to represent the unit. Help. Need to write out this equation and solve it. Spent 3 hours already!! \n" ); document.write( "
Algebra.Com's Answer #49011 by rmromero(383)\"\" \"About 
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What is asked in the problem?
\n" ); document.write( "Find the original number
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\n" ); document.write( "Given:
\n" ); document.write( "The value of a certain 2 digit number is 5 times the sum of its digits
\n" ); document.write( "the number is reversed, the resulting number is 9 more than the original number.
\n" ); document.write( "\n" ); document.write( "Representation:
\n" ); document.write( "T = tens digit
\n" ); document.write( "U = unit digit
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\n" ); document.write( "Write an Equation using the given sentence. since tens digit means t(10) and unit digit means u(1), 10t + u = the original two digit number.
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The value of a certain 2 digit number is 5 times the sum of its digits
\n" ); document.write( "10t + u = 5(t+u)
\n" ); document.write( "Simplify the equation
\n" ); document.write( "10t + u = 5t + 5u
\n" ); document.write( "5t - 4u = 0
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If the number is reversed u became the tens digit and t became the unit digit. u(10) for tens digit and t(1) for unit digit when the number is reversed. 10u + t = number is reversed
\n" ); document.write( "the number is reversed, the resulting number is 9 more than the original number.
\n" ); document.write( "10u + t = (10t + u) + 9
\n" ); document.write( "simplify the equation.
\n" ); document.write( "9u - 9t = 9
\n" ); document.write( "u - t = 1\r
\n" ); document.write( "\n" ); document.write( "Solve the variable using substitution method.
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\n" ); document.write( "Here are the Steps using Substition method
\n" ); document.write( "1. In either equation, solve for one variable in terms of the other.
\n" ); document.write( "u - t = 1
\n" ); document.write( "u = t + 1\r
\n" ); document.write( "\n" ); document.write( "2. Substitute for that variable in the other equation. Solve.
\n" ); document.write( "5t - 4u = 0
\n" ); document.write( "5t - 4(t+1) = 0
\n" ); document.write( "5t - 4t -4 = 0
\n" ); document.write( "t = 4
\n" ); document.write( "3. Substitute the result from step 2 in either equation. Solve for the other variable.
\n" ); document.write( "u = t + 1 , t=4
\n" ); document.write( "u = 4 + 1
\n" ); document.write( "u = 5\r
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\n" ); document.write( "\n" ); document.write( "4. Check the solution in both original equations.
\n" ); document.write( "5t - 4u = 0, t = 4 , u = 5
\n" ); document.write( "5(4) - 4(5) = 0
\n" ); document.write( "20 - 20 = 0
\n" ); document.write( "0 = 0 ----------> True\r
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\n" ); document.write( "u - t = 1, t = 4 , u = 5
\n" ); document.write( "5 - 4 = 1
\n" ); document.write( "1 = 1 ---------->> True\r
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Therefor the tens digit is 4 and the unit digit is 5
\n" ); document.write( "the original number now is 10t + u when t = 4 and u = 5
\n" ); document.write( "10(4) + 5 = 40 + 5 = 45\r
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