At a school carnival, each woman received 4 packets of sweets and each man received 6 packets of sweets. Each accompanying child received 7 packets of sweets. ²₅ 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 2004 packets of sweets were given away, how many people were there at the carnival?

Women	Men	Child
3x11 = 33 u		2x11 = 22 u
3x3 = 9 u	8x3 = 24 u	22 u

	Women	Men	Child
Number	9 u	24 u	22 u
Value	4	6	7
Total Value	36 u	144 u	154 u

Fraction of the people who were adults
= 1 - ²₅
= ³₅

The number of adults is the combined repeated identity. Make the number of adults the same.  LCM of 11 and 3 is 33. 

Number of packets of sweets given away
= 9 u x 4 + 24 u x 6 + 22 u x 7
= 36 u + 144 u + 154 u
= 334 u

334 u = 2004

1 u = 2004 ÷ 334 = 6

Number of people at the carnival
= 33 u + 22 u
= 55 u
= 55 x 6
= 330

Answer(s): 330