At a school carnival, each girl received 4 packets of mini cupcakes and each boy received 6 packets of mini cupcakes. Each accompanying adult received 7 packets of mini cupcakes. ²₉ of the people at the school carnival were adults. The ratio of the number of girls to the number of boys at the carnival was 3 : 8. Given that only 4018 packets of mini cupcakes were given away, how many people were there at the carnival?

Girls	Boys	Adults
7x11 = 77 u		2x11 = 22 u
3x7 = 21 u	8x7 = 56 u	22 u

	Girls	Boys	Adults
Number	21 u	56 u	22 u
Value	4	6	7
Total Value	84 u	336 u	154 u

Fraction of the people who were children
= 1 - ²₉
= ⁷₉

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 11 and 7 is 77. 

Number of packets of mini cupcakes given away
= 21 u x 4 + 56 u x 6 + 22 u x 7
= 84 u + 336 u + 154 u
= 574 u

574 u = 4018

1 u = 4018 ÷ 574 = 7

Number of people at the carnival
= 77 u + 22 u
= 99 u
= 99 x 7
= 693

Answer(s): 693