At a school carnival, each woman received 3 packets of sweets and each man received 5 packets of sweets. Each accompanying child received 6 packets of sweets. ⁴₉ of the people at the school carnival were child. The ratio of the number of women to the number of men at the carnival was 3 : 5. Given that only 3620 packets of sweets were given away, how many people were there at the carnival?

Women	Men	Child
5x8 = 40 u		4x8 = 32 u
3x5 = 15 u	5x5 = 25 u	32 u

	Women	Men	Child
Number	15 u	25 u	32 u
Value	3	5	6
Total Value	45 u	125 u	192 u

Fraction of the people who were adults
= 1 - ⁴₉
= ⁵₉

The number of adults is the combined repeated identity. Make the number of adults the same.  LCM of 8 and 5 is 40. 

Number of packets of sweets given away
= 15 u x 3 + 25 u x 5 + 32 u x 6
= 45 u + 125 u + 192 u
= 362 u

362 u = 3620

1 u = 3620 ÷ 362 = 10

Number of people at the carnival
= 40 u + 32 u
= 72 u
= 72 x 10
= 720

Answer(s): 720