At a school carnival, each man received 2 packets of candy canes and each woman received 4 packets of candy canes. Each accompanying child received 5 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 3 : 7. Given that only 2704 packets of candy canes were given away, how many people were there at the carnival?

Men	Women	Child
7x10 = 70 u		2x10 = 20 u
3x7 = 21 u	7x7 = 49 u	20 u

	Men	Women	Child
Number	21 u	49 u	20 u
Value	2	4	5
Total Value	42 u	196 u	100 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 10 and 7 is 70. 

Number of packets of candy canes given away
= 21 u x 2 + 49 u x 4 + 20 u x 5
= 42 u + 196 u + 100 u
= 338 u

338 u = 2704

1 u = 2704 ÷ 338 = 8

Number of people at the carnival
= 70 u + 20 u
= 90 u
= 90 x 8
= 720

Answer(s): 720