document.write( "Question 309420: The sum of the digits of a certain two digit number is 7. The reversing digit increase the number by 9 \n" ); document.write( "

Algebra.Com's Answer #221313 by Stitch(470) $\"\"$ $\"About$

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Set-Up:
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\n" ); document.write( "Equation 1: $\"A+%2B+B+=+7\"$
\n" ); document.write( "Equation 2: $\"10A+%2B+B+%2B+9+=+A+%2B+10B\"$
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\n" ); document.write( "Solution:
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\n" ); document.write( "Solve equation 1 for one of the variables
\n" ); document.write( "I solved for B
\n" ); document.write( "Equation 1: $\"A+%2B+B+=+7\"$
\n" ); document.write( " $\"B+=+7+-+A\"$
\n" ); document.write( "Now plug (7 - A) into equation 2 for B
\n" ); document.write( "Equation 2: $\"10A+%2B+B+%2B+9+=+A+%2B+10B\"$
\n" ); document.write( " $\"10A+%2B+%287+-+A%29+%2B+9+=+A+%2B+10%2A%287+-+A%29\"$ Simplify
\n" ); document.write( " $\"10A+%2B+7+-+A+%2B+9+=+A+%2B+70+-+10A\"$ Simplify
\n" ); document.write( " $\"9A+%2B+16+=+70+-+9A\"$ Add 9A to both sides
\n" ); document.write( " $\"18A+%2B+16+=+70\"$ Subtract 16 from both sides
\n" ); document.write( " $\"18A+=+54\"$ Divide both sides by 18
\n" ); document.write( " $\"highlight%28A+=+3%29\"$
\n" ); document.write( "---------------------
\n" ); document.write( "Now plug 3 into equation 1 for A
\n" ); document.write( " $\"B+=+7+-+A\"$
\n" ); document.write( " $\"B+=+7+-+3\"$
\n" ); document.write( " $\"highlight_green%28B+=+4%29\"$ \n" ); document.write( "

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