document.write( "Question 1012476: a number is composed of two digits the difference of whose squares is 20. if the digits are interchanged the resulting number is 18 less than the original number. find the number. \n" ); document.write( "

Algebra.Com's Answer #628410 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+t+\"$ = the tens digit
\n" ); document.write( "Let $\"+u+\"$ = the units digit
\n" ); document.write( "-------------------------
\n" ); document.write( "(1) $\"+t%5E2+-+u%5E2+=+20+\"$
\n" ); document.write( "(2) $\"+10u+%2B+t+=+10t+%2B+u+-+18+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( "(2) $\"+9t+-+9u+=+18+\"$
\n" ); document.write( "(2) $\"+t+-+u+=+2+\"$
\n" ); document.write( "(2) $\"+t+=+u+%2B+2+\"$
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( "(1) $\"%28+u+%2B+2+%29%5E2+-+u%5E2+=+20+\"$
\n" ); document.write( "(1) $\"+u%5E2+%2B+4u+%2B+4+-+u%5E2+=+20+\"$
\n" ); document.write( "(1) $\"+4u+=+16+\"$
\n" ); document.write( "(1) $\"+u+=+4+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+t+=+u+%2B+2+\"$
\n" ); document.write( "(2) $\"+t+=+4+%2B+2+\"$
\n" ); document.write( "(2) $\"+t+=+6+\"$
\n" ); document.write( "The tens digit is 6
\n" ); document.write( "The units digit is 4
\n" ); document.write( "The number is 64
\n" ); document.write( "-----------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+t%5E2+-+u%5E2+=+20+\"$
\n" ); document.write( "(1) $\"+6%5E2+-+4%5E2+=+20+\"$
\n" ); document.write( "(1) $\"+36++-+16+=+20+\"$
\n" ); document.write( "(1) $\"+20+=+20+\"$
\n" ); document.write( "OK \n" ); document.write( "

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