document.write( "Question 728956: Ben and Bob are brothers. Seven years ago Bob was twice as old as Ben. In fourteen years, Ben will be 4/5th the age of Bob. How old are Ben and Bob now? \n" ); document.write( "

Algebra.Com's Answer #445651 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+x+\"$ = Bob's age now
\n" ); document.write( "Let $\"+y+\"$ = Ben's age now
\n" ); document.write( " $\"+x+-+7+\"$ = Bob's age 7 yrs ago
\n" ); document.write( " $\"+y+-+7+\"$ = Ben's age 7 yrs ago
\n" ); document.write( " $\"+x+%2B+14+\"$ = Bob's age in 14 yrs
\n" ); document.write( " $\"+y+%2B+14+\"$ = Ben's age in 14 yrs
\n" ); document.write( "-----------------------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+x+-+7+=+2%2A%28+y+-+7+%29+\"$
\n" ); document.write( "(2) $\"+y+%2B+14+=+%284%2F5%29%2A%28+x+%2B+14+%29+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(1) $\"+x+-+7+=+2y+-+14+\"$
\n" ); document.write( "(1) $\"+x+-+2y+=+-7+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+5%2A%28+y+%2B+14+%29+=+4%2A%28+x+%2B+14+%29+\"$
\n" ); document.write( "(2) $\"+5y+%2B+70+=+4x+%2B+56+\"$
\n" ); document.write( "(2) $\"+4x+-+5y+=+14+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "Multiply both sides of (1) by $\"+-4+\"$
\n" ); document.write( "and add the equations
\n" ); document.write( "(1) $\"+-4x+%2B+8y+=+28+\"$
\n" ); document.write( "(2) $\"+4x+-+5y+=+14+\"$
\n" ); document.write( " $\"+3y+=+42+\"$
\n" ); document.write( " $\"+y+=+14+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+x+-+2y+=+-7+\"$
\n" ); document.write( "(1) $\"+x+-+2%2A14+=+-7+\"$
\n" ); document.write( "(1) $\"+x+=+28+-+7+\"$
\n" ); document.write( "(1) $\"+x+=+21+\"$
\n" ); document.write( "--------------
\n" ); document.write( "Bob is 21 and Ben is 14
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+y+%2B+14+=+%284%2F5%29%2A%28+x+%2B+14+%29+\"$
\n" ); document.write( "(2) $\"+14+%2B+14+=+%284%2F5%29%2A%28+21+%2B+14+%29+\"$
\n" ); document.write( "(2) $\"+28+=+%284%2F5%29%2A35+\"$
\n" ); document.write( "(2) $\"+28+=+28+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+x+-+7+=+2%2A%28+y+-+7+%29+\"$
\n" ); document.write( "(1) $\"+21+-+7+=+2%2A%28+14+-+7+%29+\"$
\n" ); document.write( "(1) $\"+14+=+2%2A7+\"$
\n" ); document.write( "(1) $\"+14+=+14+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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