document.write( "Question 919435: how to set up: a two digit number is 3 times the sum of its digits. the number is also 45 less than the number formed by reversing the digits of the original number. what is the original number? \n" ); document.write( "

Algebra.Com's Answer #557768 by Theo(13342) $\"\"$ $\"About$

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let x = the tens digit
\n" ); document.write( "let y = the units digit\r
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\n" ); document.write( "\n" ); document.write( "10x + y = 3 * (x + y)
\n" ); document.write( "simplify to get:
\n" ); document.write( "10x + y = 3x + 3y
\n" ); document.write( "subtract 3x from both sides of the equation to get:
\n" ); document.write( "7x + y = 3y
\n" ); document.write( "subtract y from both sides of the equation to get:
\n" ); document.write( "7x = 2y
\n" ); document.write( "divide both sides of the equaation by 2 to get:
\n" ); document.write( "y = 7x/2\r
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\n" ); document.write( "\n" ); document.write( "10x + y = 10y + x - 45
\n" ); document.write( "subtract x from both sides of the equation to get:
\n" ); document.write( "9x + y = 10y - 45
\n" ); document.write( "subtract 10y from both sides of the equation to get:
\n" ); document.write( "9x - 9y = -45
\n" ); document.write( "replace y with 7x/2 to get:
\n" ); document.write( "9x - 9 * (7x/2) = -45
\n" ); document.write( "simplify to get:
\n" ); document.write( "9x - 63x / 2 = -45
\n" ); document.write( "multiply both sides of the equation by 2 to get:
\n" ); document.write( "18x - 63x = -90
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "-45x = -90
\n" ); document.write( "divide both sides of the equation by -2 to get:
\n" ); document.write( "x = 2\r
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\n" ); document.write( "\n" ); document.write( "y = 7x/2
\n" ); document.write( "replace x with 2 to get:
\n" ); document.write( "y = (7*2)/2
\n" ); document.write( "simplify to get:
\n" ); document.write( "y = 7\r
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\n" ); document.write( "\n" ); document.write( "that's your solution.
\n" ); document.write( "x = 2
\n" ); document.write( "y = 7
\n" ); document.write( "10x + y = 27\r
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\n" ); document.write( "\n" ); document.write( "10x + y = 3 * (x+y) becomes
\n" ); document.write( "10*2 + 7 = 3 * (2 + 7) which becomes:
\n" ); document.write( "20 + 7 - 3 * 9 which becomes:
\n" ); document.write( "27 = 27 which is true.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "10x + y = 10y + x - 45 becomes:
\n" ); document.write( "10 * 2 + 7 = 10 * 7 + 2 - 45 which becomes:
\n" ); document.write( "20 + 7 = 70 + 2 - 45 which becomes:
\n" ); document.write( "27 = 72 - 45 which becomes:
\n" ); document.write( "27 = 27 which is true.\r
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\n" ); document.write( "\n" ); document.write( "everything checks out so the solution is good.\r
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\n" ); document.write( "\n" ); document.write( "you could also have done a simple logic test up front which would have told you that y had to be equal 7 and x have to be equal to 2.\r
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\n" ); document.write( "\n" ); document.write( "this is because y = 7x/2\r
\n" ); document.write( "\n" ); document.write( "when x = 2, y equal 7.
\n" ); document.write( "x had to be between 0 and 9
\n" ); document.write( "y had to be between 0 and 9.
\n" ); document.write( "x and y both had to be integers.
\n" ); document.write( "the only value of x that gave a valid value of y was x = 2.
\n" ); document.write( "all others were either out of range of not integers.\r
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