document.write( "Question 867384: there were four times as many boys as girls at a party. After 105 boys left the party, there were twice as many girls as boys left. How many children were there altogether at first? \n" ); document.write( "

Algebra.Com's Answer #522982 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+b+\"$ = the number of boys at first
\n" ); document.write( "Let $\"+g+\"$ = the number of girls at first
\n" ); document.write( "---------------------------------------------
\n" ); document.write( "(1) $\"+b+=+4g+\"$
\n" ); document.write( "(2) $\"+g+=+2%2A%28+b+-+105+%29+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+g+=+2%2A%28+4g+-+105+%29+\"$
\n" ); document.write( "(2) $\"+g+=+8g+-+210+\"$
\n" ); document.write( "(2) $\"+7g+=+210+\"$
\n" ); document.write( "(2) $\"+g+=+30+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+b+=+4g+\"$
\n" ); document.write( "(1) $\"+b+=+4%2A30+\"$
\n" ); document.write( "(1) $\"+b+=+120+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "The number of children
\n" ); document.write( "at first = $\"+b+%2B+g+\"$
\n" ); document.write( " $\"+b+%2B+g+=+120+%2B+30+\"$
\n" ); document.write( " $\"+b+%2B+g+=+150+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+g+=+2%2A%28+b+-+105+%29+\"$
\n" ); document.write( "(2) $\"+30+=+2%2A%28+120+-+105+%29+\"$
\n" ); document.write( "(2) $\"+30+=+2%2A15+\"$
\n" ); document.write( "(2) $\"+30+=+30+\"$
\n" ); document.write( "OK \n" ); document.write( "

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