At a school carnival, each boy received 2 packets of caramel apples and each girl received 3 packets of caramel apples. Each accompanying adult received 4 packets of caramel apples. ²₉ 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 5 : 8. Given that only 684 packets of caramel apples were given away, how many people were there at the carnival?

Boys	Girls	Adults
7x13 = 91 u		2x13 = 26 u
5x7 = 35 u	8x7 = 56 u	26 u

	Boys	Girls	Adults
Number	35 u	56 u	26 u
Value	2	3	4
Total Value	70 u	168 u	104 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 13 and 7 is 91. 

Number of packets of caramel apples given away
= 35 u x 2 + 56 u x 3 + 26 u x 4
= 70 u + 168 u + 104 u
= 342 u

342 u = 684

1 u = 684 ÷ 342 = 2

Number of people at the carnival
= 91 u + 26 u
= 117 u
= 117 x 2
= 234

Answer(s): 234