At a school carnival, each man received 3 packets of chocolate bars and each woman received 5 packets of chocolate bars. Each accompanying child received 7 packets of chocolate bars. 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 4424 packets of chocolate bars 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	3	5	7
Total Value	45 u	200 u	308 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 chocolate bars given away
= 15 u x 3 + 40 u x 5 + 44 u x 7
= 45 u + 200 u + 308 u
= 553 u

553 u = 4424

1 u = 4424 ÷ 553 = 8

Number of people at the carnival
= 55 u + 44 u
= 99 u
= 99 x 8
= 792

Answer(s): 792