document.write( "Question 691413: The sum of the digits of a two digit number is 10. The number formed by reversing the number is 4 less than 5 times the number. Find the original number?\r
\n" ); document.write( "\n" ); document.write( "Can you please help me out with this question I really don't understand? thanks in advance \n" ); document.write( "

Algebra.Com's Answer #426679 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the tens digit = $\"+a+\"$
\n" ); document.write( "Let the units digit = $\"+b+\"$
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\n" ); document.write( "The number looks like ab, like the number 36,
\n" ); document.write( "but the value of the number is $\"+10a+%2B+b+\"$ ,
\n" ); document.write( "the same way that $\"+36+=+3%2A10+%2B+6+\"$
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\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( "This is just talking about the digits and not the value
\n" ); document.write( "of the number
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\n" ); document.write( "The VALUE of the number, as I said, is $\"+10a+%2B+b+\"$
\n" ); document.write( "and the value of the number formed by reversing the digits is
\n" ); document.write( " $\"+10b+%2B+a+\"$
\n" ); document.write( "You are told that
\n" ); document.write( "(2) $\"+10b+%2B+a+=+5%2A%28+10a+%2B+b+%29+-+4+\"$
\n" ); document.write( "You have 2 equations, (1) and (2), and 2 unknowns, so
\n" ); document.write( "it is solvable.
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\n" ); document.write( "(2) $\"+10b+%2B+a+=+50a+%2B+5b+-+4+\"$
\n" ); document.write( "(2) $\"+5b+=+49a+-+4+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( "(1) $\"+b+=+10+-+a+\"$
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+5b+=+49a+-+4+\"$
\n" ); document.write( "(2) $\"+5%2A%28+10+-+a+%29+=+49a+-+4+\"$
\n" ); document.write( "(2) $\"+50+-+5a+=+49a+-+4+\"$
\n" ); document.write( "(2) $\"+54a+=+54+\"$
\n" ); document.write( "(2) $\"+a+=+1+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+b+=+10+-+a+\"$
\n" ); document.write( "(1) $\"+b+=+10+-+1+\"$
\n" ); document.write( "(1) $\"+b+=+9+\"$
\n" ); document.write( "The number is 19
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+10b+%2B+a+=+5%2A%28+10a+%2B+b+%29+-+4+\"$
\n" ); document.write( "(2) $\"+10%2A9+%2B+1+=+5%2A%28+10%2A1+%2B+9+%29+-+4+\"$
\n" ); document.write( "(2) $\"+91+=+5%2A19+-+4+\"$
\n" ); document.write( "(2) $\"+91+=+95+-+4+\"$
\n" ); document.write( "(2) $\"+91+=+91+\"$
\n" ); document.write( "OK\r
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