document.write( "Question 715216: The sum of the digits of a two digit number is ten. The original number is two more than five times the units digit. Find this number. \n" ); document.write( "

Algebra.Com's Answer #439391 by KMST(5328) $\"\"$ $\"About$

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$\"a\"$ = tens digit
\n" ); document.write( " $\"b\"$ = units digit
\n" ); document.write( "The value of the number is $\"10a%2Bb\"$
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\n" ); document.write( "\"The sum of the digits of a two digit number is ten\" translates as
\n" ); document.write( " $\"a%2Bb=10\"$
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\n" ); document.write( "\"The original number is two more than five times the units digit\" translates as
\n" ); document.write( " $\"10a%2Bb=5%2Ab%2B2\"$ --> $\"10a%2Bb=5b%2B2\"$ --> $\"10a%2Bb-5b=5b%2B2-5b\"$ --> $\"10a-4b=2\"$
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\n" ); document.write( "We need to solve the system $\"system%28a%2Bb=10%2C10a-4b=2%29\"$
\n" ); document.write( "we can solve the first equation for $\"a\"$ and substitute the expression found for $\"a\"$ in the second equation to find $\"b\"$
\n" ); document.write( " $\"a%2Bb=10\"$ --> $\"a=10-b\"$
\n" ); document.write( " $\"10a-4b=2\"$ --> $\"10%2810-b%29-4b=2\"$ --> $\"100-10b-4b=2\"$ --> $\"100-14b=2\"$ --> $\"100-14b%2B14b-2=2%2B14b-2\"$ --> $\"100-2=14b\"$ --> $\"98=14b\"$ --> $\"98%2F14=14b%2F14\"$ --> $\"highlight%28b=7%29\"$
\n" ); document.write( "Now we substitute that value into one of the equations to find $\"a\"$ :
\n" ); document.write( " $\"a%2Bb=10\"$ --> $\"a%2B7=10\"$ --> $\"a=10-7\"$ --> $\"highlight%28a=3%29\"$
\n" ); document.write( "The number is $\"highlight%2837%29\"$ \n" ); document.write( "

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