document.write( "Question 559533: In the cafeteria, the ratio of the number of girls to boys is 6:7. When 117 girls enter the cafeteria, the new ratio of girls to boys became 7:6. How many pupils were in the cafeteria at first? \n" ); document.write( "

Algebra.Com's Answer #363457 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+g%2Fb+\"$ = the original ratio of girls to boys
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+g%2Fb+=+6%2F7+\"$
\n" ); document.write( "(2) $\"+%28+g+%2B+117+%29%2Fb+=+7%2F6+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "(1) $\"+7g+=+6b+\"$
\n" ); document.write( "(1) $\"+b+=+%287%2F6%29%2Ag+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+6%2A%28+g+%2B+117+%29+=+7b+\"$
\n" ); document.write( "(2) $\"+6g+%2B+702+=+7%2A%287%2F6%29%2Ag+\"$
\n" ); document.write( "(2) $\"+36g+%2B+4212+=+49g+\"$
\n" ); document.write( "(2) $\"+13g+=+4212+\"$
\n" ); document.write( "(2) $\"+g+=+324+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+b+=+%287%2F6%29%2Ag+\"$
\n" ); document.write( "(1) $\"+b+=+%287%2F6%29%2A324+\"$
\n" ); document.write( "(1) $\"+b+=+378+\"$
\n" ); document.write( "There were $\"+324+%2B+378+=+702+\"$
\n" ); document.write( "pupils in the cafe at first
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+%28+g+%2B+117+%29%2Fb+=+7%2F6+\"$
\n" ); document.write( "(2) $\"+%28+324+%2B+117+%29%2F378+=+7%2F6+\"$
\n" ); document.write( "(2) $\"+441%2F378+=+7%2F6+\"$
\n" ); document.write( "(2) $\"+441%2A6+=+7%2A378+\"$
\n" ); document.write( "(2) $\"+2646+=+2646+\"$
\n" ); document.write( "OK \n" ); document.write( "

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