At a school carnival, each woman received 5 packets of caramel apples and each man received 7 packets of caramel apples. Each accompanying child received 8 packets of caramel apples. 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 : 8. Given that only 2828 packets of caramel apples were given away, how many people were there at the carnival?

Women	Men	Child
5x11 = 55 u		4x11 = 44 u
3x5 = 15 u	8x5 = 40 u	44 u

	Women	Men	Child
Number	15 u	40 u	44 u
Value	5	7	8
Total Value	75 u	280 u	352 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 11 and 5 is 55. 

Number of packets of caramel apples given away
= 15 u x 5 + 40 u x 7 + 44 u x 8
= 75 u + 280 u + 352 u
= 707 u

707 u = 2828

1 u = 2828 ÷ 707 = 4

Number of people at the carnival
= 55 u + 44 u
= 99 u
= 99 x 4
= 396

Answer(s): 396