document.write( "Question 194932This question is from textbook Algebra and Trigonometry Structure and Method Book 2
\n" ); document.write( ": The product of a two-digit number and its tens digit is 285. The units digit is two more than the tens digit. What is the original number? \n" ); document.write( "
Algebra.Com's Answer #146231 by ankor@dixie-net.com(22740)\"\" \"About 
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Let x = the 10's digit
\n" ); document.write( "Let y = the units
\n" ); document.write( "then
\n" ); document.write( "10x + y = the two digit number
\n" ); document.write( ";
\n" ); document.write( "\"The product of a two-digit number and its tens digit is 285\".
\n" ); document.write( "x(10x + y) = 285
\n" ); document.write( ":
\n" ); document.write( "\" The units digit is two more than the tens digit.\"
\n" ); document.write( "y = x+2
\n" ); document.write( ":
\n" ); document.write( "Substitute (x+2) for y in the 1st equation
\n" ); document.write( "x(10x + (x+2)) = 285
\n" ); document.write( ":
\n" ); document.write( "x(11x + 2) = 285
\n" ); document.write( ":
\n" ); document.write( "11x^2 + 2x = 285
\n" ); document.write( ":
\n" ); document.write( "11x^2 + 2x - 285 = 0; a quadratic equation
\n" ); document.write( "Factors to:
\n" ); document.write( "(11x + 57)(x - 5) = 0
\n" ); document.write( "Positive solution
\n" ); document.write( "x = 5
\n" ); document.write( "then
\n" ); document.write( "y = 5 + 2
\n" ); document.write( "y = 7
\n" ); document.write( ":
\n" ); document.write( "the original number = 57
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check solution:
\n" ); document.write( "5(10(5) + 7) =
\n" ); document.write( "5(57) = 285\r
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