At a school carnival, each girl received 5 packets of candy canes and each boy received 7 packets of candy canes. Each accompanying adult received 8 packets of candy canes. 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 : 8. Given that only 4650 packets of candy canes were given away, how many people were there at the carnival?

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

	Girls	Boys	Adults
Number	35 u	56 u	26 u
Value	5	7	8
Total Value	175 u	392 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 candy canes given away
= 35 u x 5 + 56 u x 7 + 26 u x 8
= 175 u + 392 u + 208 u
= 775 u

775 u = 4650

1 u = 4650 ÷ 775 = 6

Number of people at the carnival
= 91 u + 26 u
= 117 u
= 117 x 6
= 702

Answer(s): 702