At a school carnival, each boy received 5 packets of mini cupcakes and each girl received 7 packets of mini cupcakes. Each accompanying adult received 9 packets of mini cupcakes. ²₅ of the people at the school carnival were adults. The ratio of the number of boys to the number of girls at the carnival was 4 : 7. Given that only 2430 packets of mini cupcakes were given away, how many people were there at the carnival?

Boys	Girls	Adults
3x11 = 33 u		2x11 = 22 u
4x3 = 12 u	7x3 = 21 u	22 u

	Boys	Girls	Adults
Number	12 u	21 u	22 u
Value	5	7	9
Total Value	60 u	147 u	198 u

Fraction of the people who were children
= 1 - ²₅
= ³₅

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 11 and 3 is 33. 

Number of packets of mini cupcakes given away
= 12 u x 5 + 21 u x 7 + 22 u x 9
= 60 u + 147 u + 198 u
= 405 u

405 u = 2430

1 u = 2430 ÷ 405 = 6

Number of people at the carnival
= 33 u + 22 u
= 55 u
= 55 x 6
= 330

Answer(s): 330