document.write( "Question 181909: The tens' digit of a certain two-digit number is twice the units' digit. The difference between the square of the number and the square of the number obtained by reversing the digits is 297. What is the number? \n" ); document.write( "
Algebra.Com's Answer #136546 by ankor@dixie-net.com(22740)\"\" \"About 
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The tens' digit of a certain two-digit number is twice the units' digit.
\n" ); document.write( " The difference between the square of the number and the square of the number
\n" ); document.write( " obtained by reversing the digits is 297. What is the number?
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\n" ); document.write( "Let x = 10's digit
\n" ); document.write( "Let y = units digit
\n" ); document.write( "then
\n" ); document.write( "10x + y = the two-digit number
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\n" ); document.write( "Write an equation for each statement:
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\n" ); document.write( "\"The tens' digit of a certain two-digit number is twice the units' digit.\"
\n" ); document.write( "x = 2y
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\n" ); document.write( "\" The difference between the square of the number and the square of the number obtained by reversing the digits is 297.\"
\n" ); document.write( "(10x-y)^2 - (10y-x)^2 = 297
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\n" ); document.write( "(100x^2 - 20xy + y^2) - (100y^2 - 20xy + x^2) = 297
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\n" ); document.write( "100x^2 - 20xy + y^2 - 100y^2 + 20xy - x^2 = 297
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\n" ); document.write( "100x^2 - x^2 - 20xy + 20xy + y^2 - 100y^2 = 297
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\n" ); document.write( "99x^2 - 99y^2 = 297
\n" ); document.write( ":
\n" ); document.write( "simplify, divide equation by 99
\n" ); document.write( "x^2 - y^2 = 3
\n" ); document.write( ":
\n" ); document.write( "Substitute 2y for x
\n" ); document.write( "(2y)^2 - y^2 = 3
\n" ); document.write( ":
\n" ); document.write( "4y^2 - y^2 = 3
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\n" ); document.write( "3y^2 = 3
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\n" ); document.write( "y^2 = \"3%2F3\"
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\n" ); document.write( "y^2 = 1,
\n" ); document.write( "Therefore
\n" ); document.write( "y = 1 and x = 2: 21 is the number
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\n" ); document.write( "Check
\n" ); document.write( " 21^2 - 12^2 =
\n" ); document.write( "441 - 144 - 297\r
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