At a school carnival, each girl received 5 packets of lollipops and each boy received 6 packets of lollipops. Each accompanying adult received 7 packets of lollipops. 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 5 : 7. Given that only 5096 packets of lollipops were given away, how many people were there at the carnival?

Girls	Boys	Adults
7x12 = 84 u		2x12 = 24 u
5x7 = 35 u	7x7 = 49 u	24 u

	Girls	Boys	Adults
Number	35 u	49 u	24 u
Value	5	6	7
Total Value	175 u	294 u	168 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 12 and 7 is 84. 

Number of packets of lollipops given away
= 35 u x 5 + 49 u x 6 + 24 u x 7
= 175 u + 294 u + 168 u
= 637 u

637 u = 5096

1 u = 5096 ÷ 637 = 8

Number of people at the carnival
= 84 u + 24 u
= 108 u
= 108 x 8
= 864

Answer(s): 864