document.write( "Question 624877: the sum of the numerator and denominator of a fraction is 11.if 1 is added to the numerator and 2 is subtracted from the denominator,it becomes 2/3.the fraction is \n" ); document.write( "

Algebra.Com's Answer #393147 by josmiceli(19441) $\"\"$ $\"About$

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Let the fraction = $\"+a%2Fb+\"$
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=++11+\"$
\n" ); document.write( "(2) $\"+%28+a+%2B+1+%29+%2F+%28+b+-+2+%29+=+2%2F3+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "Multiply both sides of (2) by $\"+3%2A%28+b+-+2+%29+\"$
\n" ); document.write( "(2) $\"+3%2A%28+a+%2B+1+%29++=+2%2A%28+b+-+2+%29+\"$
\n" ); document.write( "(2) $\"+3a+%2B+3+=+2b+-+4+\"$
\n" ); document.write( "(2) $\"+3a+-+2b+=+-7+\"$
\n" ); document.write( "------------------
\n" ); document.write( "Multiply both sides of (1) by $\"+2+\"$
\n" ); document.write( "and add the equations
\n" ); document.write( "(1) $\"+2a+%2B+2b+=++22+\"$
\n" ); document.write( "(2) $\"+3a+-+2b+=+-7+\"$
\n" ); document.write( " $\"+5a+=+15+\"$
\n" ); document.write( " $\"+a+=+3+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=++11+\"$
\n" ); document.write( "(1) $\"+3+%2B+b+=++11+\"$
\n" ); document.write( "(1) $\"+b+=+8+\"$
\n" ); document.write( "The fraction is 3/8
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+a+%2B+1+%29+%2F+%28+b+-+2+%29+=+2%2F3+\"$
\n" ); document.write( "(2) $\"+%28+3+%2B+1+%29+%2F+%28+8+-+2+%29+=+2%2F3+\"$
\n" ); document.write( "(2) $\"+4%2F6+=+2%2F3+\"$
\n" ); document.write( "(2) $\"+2%2F3+=+2%2F3+\"$
\n" ); document.write( "OK\r
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