document.write( "Question 826957: A girl is five years older than a boy. Nine years ago, the boy's age was two thirds the girl's age. The boy's age is...? \n" ); document.write( "

Algebra.Com's Answer #498355 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+g+\"$ = the girl's age now
\n" ); document.write( "Let $\"+b+\"$ = the boy's age now
\n" ); document.write( "-----------------
\n" ); document.write( "(1) $\"+g+=+b+%2B+5+\"$
\n" ); document.write( "(2) $\"+b+-+9+=+%282%2F3%29%2A%28+g+-+9+%29+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "(2) $\"+3%2A%28+b+-+9+%29+=+2%2A%28+g+-+9+%29+\"$
\n" ); document.write( "(2) $\"+3b+-+27+=+2g+-+18+\"$
\n" ); document.write( "(2) $\"+3b+-+2g+=+9+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+-b+%2B+g+=+5+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "Multiply both sides of (1) by $\"2\"$
\n" ); document.write( "and add the equations
\n" ); document.write( "(2) $\"+3b+-+2g+=+9+\"$
\n" ); document.write( "(1) $\"+-2b+%2B+2g+=+10+\"$
\n" ); document.write( " $\"+b+=+19+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+g+=+b+%2B+5+\"$
\n" ); document.write( "(1) $\"+g+=+19+%2B+5+\"$
\n" ); document.write( "(1) $\"+g+=+24+\"$
\n" ); document.write( "The boys age is 19
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+b+-+9+=+%282%2F3%29%2A%28+g+-+9+%29+\"$
\n" ); document.write( "(2) $\"+19+-+9+=+%282%2F3%29%2A%28+24+-+9+%29+\"$
\n" ); document.write( "(2) $\"+10+=+%282%2F3%29%2A15+\"$
\n" ); document.write( "(2) $\"+10+=+10+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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