document.write( "Question 1128046: The sum of the ages of husband & his wife is four times the sum of the agesof their children . four years ago , the ratio of sum of their ages to the sum of their children was 18:1 . two years hence the ratio will be 3:1 .how many children do they have ? \n" ); document.write( "

Algebra.Com's Answer #744561 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+x+\"$ = sum of husband and wife's ages
\n" ); document.write( "Let $\"+y+\"$ = sum of their children's ages
\n" ); document.write( "Let $\"+n+\"$ = the number of children
\n" ); document.write( "--------------------
\n" ); document.write( "(1) $\"+x+=+4y+\"$
\n" ); document.write( "(2) $\"+%28+x+-+8+%29+%2F+%28+y+-+4n+%29+=+18%2F1+\"$
\n" ); document.write( "(3) $\"+%28+x+%2B+4+%29+%2F+%28+y+%2B+2n+%29+=+3%2F1+\"$
\n" ); document.write( "( note that each parent and each child's age get
\n" ); document.write( "added to by number of years in future. The
\n" ); document.write( "opposite is true going into past )
\n" ); document.write( "------------------------------------------
\n" ); document.write( "(2) $\"+x+-+8+=+18%2A%28+y+-+4n+%29+\"$
\n" ); document.write( "(2) $\"+x+-+8+=+18y+-+72n+\"$
\n" ); document.write( "(2) $\"+x+-+18y+=+8+-+72n+\"$
\n" ); document.write( "Plug (1) into (2)
\n" ); document.write( "(2) $\"+4y+-+18y+=+8+-+72n+\"$
\n" ); document.write( "(2) $\"+-14y+=+-72n+%2B8+\"$
\n" ); document.write( "(2) $\"+7y+=+36n+-+4+\"$
\n" ); document.write( "-------------------------------
\n" ); document.write( "(3) $\"+x+%2B+4+=+3%2A%28+y+%2B+2n+%29+\"$
\n" ); document.write( "(3) $\"+x+%2B+4+=+3y+%2B+6n+\"$
\n" ); document.write( "(3) $\"+x+-+3y+=+6n+-+4+\"$
\n" ); document.write( "(3) $\"+4y+-+3y+=+6n+-+4+\"$
\n" ); document.write( "(3) $\"+y+=+6n+-+4+\"$
\n" ); document.write( "-------------------------------
\n" ); document.write( "Multiply both sides of (3) by $\"+6+\"$
\n" ); document.write( "and subtract (3) from (2)
\n" ); document.write( "(2) $\"+7y+=+36n+-+4+\"$
\n" ); document.write( "(3) $\"+-6y+=+-36n+%2B+24+\"$
\n" ); document.write( "-------------------------------
\n" ); document.write( " $\"+y+=+20+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+x+=+4y+\"$
\n" ); document.write( " $\"+x+=+80+\"$
\n" ); document.write( "------------------
\n" ); document.write( "(3) $\"+%28+x+%2B+4+%29+%2F+%28+y+%2B+2n+%29+=+3%2F1+\"$
\n" ); document.write( "(3) $\"+%28+80+%2B+4+%29+%2F+%28+20+%2B+2n+%29+=+3%2F1+\"$
\n" ); document.write( "(3) $\"+84+=+3%2A%28+20+%2B+2n+%29+\"$
\n" ); document.write( "(3) $\"+84+=+60+%2B+6n+\"$
\n" ); document.write( "(3) $\"+6n+=+24+\"$
\n" ); document.write( "(3) $\"+n+=+4+\"$
\n" ); document.write( "They have 4 children
\n" ); document.write( "-----------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+x+-+8+%29+%2F+%28+y+-+4n+%29+=+18%2F1+\"$
\n" ); document.write( "(2) $\"+%28+80+-+8+%29+%2F+%28+20+-+4n+%29+=+18+\"$
\n" ); document.write( "(2) $\"+72+=+18%2A%28+20+-+4n+%29+\"$
\n" ); document.write( "(2) $\"+72+=+360+-+72n+\"$
\n" ); document.write( "(2) $\"+72n+=+288+\"$
\n" ); document.write( "(2) $\"+n+=+4+\"$
\n" ); document.write( "OK
\n" ); document.write( "Get a 2nd opinion if this is incorrect\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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