document.write( "Question 527452: The difference of the digits of a two-digit number is 4. Find the number if the product of the digits is 45. \n" ); document.write( "

Algebra.Com's Answer #348911 by swincher4391(1107) $\"\"$ $\"About$

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Let our answer be in the form 10x + y. We'll use this later.\r
\n" ); document.write( "\n" ); document.write( "x-y = 4 --> x = 4+y
\n" ); document.write( "xy = 45\r
\n" ); document.write( "\n" ); document.write( "(4+y)y = 45\r
\n" ); document.write( "\n" ); document.write( "4y + y^2 = 45\r
\n" ); document.write( "\n" ); document.write( "y^2 + 4y -45 = 0\r
\n" ); document.write( "\n" ); document.write( "(y+9)(y-5) = 0\r
\n" ); document.write( "\n" ); document.write( "This gives us answers of y=-9 and y=5. Since a negative answer won't give us the answer we're looking for, then y = 5 is the only logical solution.\r
\n" ); document.write( "\n" ); document.write( "Plug y = 5 back into either equation.\r
\n" ); document.write( "\n" ); document.write( "x(5) = 45\r
\n" ); document.write( "\n" ); document.write( "5x = 45\r
\n" ); document.write( "\n" ); document.write( "x = 9\r
\n" ); document.write( "\n" ); document.write( "Going back to our 10x+y...\r
\n" ); document.write( "\n" ); document.write( "10(9) + 5 = 95
\n" ); document.write( "Thus our answer is 95. \n" ); document.write( "

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