document.write( "Question 677041: The numerator of a fraction is 3 less than the denominator. If 5 is added to both the numerator and denominator, the value resulting fraction is 3/4. Find the original fraction \n" ); document.write( "

Algebra.Com's Answer #420653 by josmiceli(19441) $\"\"$ $\"About$

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Let the fraction = $\"+a%2Fb+\"$
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+=+b+-+3+\"$
\n" ); document.write( "(2) $\"+%28+a+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F4+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+%28+b+-+3+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F4+\"$
\n" ); document.write( "(2) $\"+%28+b+%2B+2+%29+%2F+%28+b+%2B+5+%29+=+3%2F4+\"$
\n" ); document.write( "Multiply both sides by $\"+4%2A%28+b-5+%29+\"$
\n" ); document.write( "(2) $\"+4%2A%28+b+%2B+2+%29+=+3%2A%28+b+%2B+5+%29+\"$
\n" ); document.write( "(2) $\"+4b+%2B+8+=+3b+%2B+15+\"$
\n" ); document.write( "(2) $\"+b+=+7+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+=+b+-+3+\"$
\n" ); document.write( "(1) $\"+a+=+7+-+3+\"$
\n" ); document.write( "(1) $\"+a+=+4+\"$
\n" ); document.write( "The fraction is $\"+a%2Fb+=+4%2F7+\"$
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+%28+a+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F4+\"$
\n" ); document.write( "(2) $\"+%28+4+%2B+5+%29+%2F+%28+7+%2B+5+%29+=+3%2F4+\"$
\n" ); document.write( "(2) $\"+9+%2F+12+=+3%2F4+\"$
\n" ); document.write( "(2) $\"+3%2F4+=+3%2F4+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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