At a school carnival, each man received 2 packets of caramel apples and each woman received 4 packets of caramel apples. Each accompanying child received 6 packets of caramel apples. ⁴₉ 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 : 8. Given that only 2724 packets of caramel apples were given away, how many people were there at the carnival?

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

	Men	Women	Child
Number	15 u	40 u	44 u
Value	2	4	6
Total Value	30 u	160 u	264 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 2 + 40 u x 4 + 44 u x 6
= 30 u + 160 u + 264 u
= 454 u

454 u = 2724

1 u = 2724 ÷ 454 = 6

Number of people at the carnival
= 55 u + 44 u
= 99 u
= 99 x 6
= 594

Answer(s): 594