At a school carnival, each boy received 5 packets of caramel apples and each girl received 6 packets of caramel apples. Each accompanying adult received 8 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 2157 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	5	6	8
Total Value	175 u	336 u	208 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 5 + 56 u x 6 + 26 u x 8
= 175 u + 336 u + 208 u
= 719 u

719 u = 2157

1 u = 2157 ÷ 719 = 3

Number of people at the carnival
= 91 u + 26 u
= 117 u
= 117 x 3
= 351

Answer(s): 351