At a school carnival, each man received 4 packets of candy canes and each woman received 5 packets of candy canes. Each accompanying child received 7 packets of candy canes. ²₉ of the people at the school carnival were child. The ratio of the number of men to the number of women at the carnival was 5 : 8. Given that only 3612 packets of candy canes were given away, how many people were there at the carnival?

Men	Women	Child
7x13 = 91 u		2x13 = 26 u
5x7 = 35 u	8x7 = 56 u	26 u

	Men	Women	Child
Number	35 u	56 u	26 u
Value	4	5	7
Total Value	140 u	280 u	182 u

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

The number of adults is the combined repeated identity. Make the number of adults the same.  LCM of 13 and 7 is 91. 

Number of packets of candy canes given away
= 35 u x 4 + 56 u x 5 + 26 u x 7
= 140 u + 280 u + 182 u
= 602 u

602 u = 3612

1 u = 3612 ÷ 602 = 6

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

Answer(s): 702