SOLUTION: 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 cafe

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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 cafe      Log On


   



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?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +g%2Fb+ = the original ratio of girls to boys
given:
(1) +g%2Fb+=+6%2F7+
(2) +%28+g+%2B+117+%29%2Fb+=+7%2F6+
---------------------
(1) +7g+=+6b+
(1) +b+=+%287%2F6%29%2Ag+
and
(2) +6%2A%28+g+%2B+117+%29+=+7b+
(2) +6g+%2B+702+=+7%2A%287%2F6%29%2Ag+
(2) +36g+%2B+4212+=+49g+
(2) +13g+=+4212+
(2) +g+=+324+
and
(1) +b+=+%287%2F6%29%2Ag+
(1) +b+=+%287%2F6%29%2A324+
(1) +b+=+378+
There were +324+%2B+378+=+702+
pupils in the cafe at first
check answer:
(2) +%28+g+%2B+117+%29%2Fb+=+7%2F6+
(2) +%28+324+%2B+117+%29%2F378+=+7%2F6+
(2) +441%2F378+=+7%2F6+
(2) +441%2A6+=+7%2A378+
(2) +2646+=+2646+
OK