At a school carnival, each man received 5 packets of candy canes and each woman received 6 packets of candy canes. Each accompanying child received 8 packets of candy canes. ³₇ 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 2416 packets of candy canes were given away, how many people were there at the carnival?

Men	Women	Child
4x13 = 52 u		3x13 = 39 u
5x4 = 20 u	8x4 = 32 u	39 u

	Men	Women	Child
Number	20 u	32 u	39 u
Value	5	6	8
Total Value	100 u	192 u	312 u

Fraction of the people who were adults
= 1 - ³₇
= ⁴₇

The number of adults is the combined repeated identity. Make the number of adults the same.  LCM of 13 and 4 is 52. 

Number of packets of candy canes given away
= 20 u x 5 + 32 u x 6 + 39 u x 8
= 100 u + 192 u + 312 u
= 604 u

604 u = 2416

1 u = 2416 ÷ 604 = 4

Number of people at the carnival
= 52 u + 39 u
= 91 u
= 91 x 4
= 364

Answer(s): 364