At a school carnival, each woman received 2 packets of sweets and each man received 3 packets of sweets. Each accompanying child received 4 packets of sweets. ²₇ 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 4 : 7. Given that only 932 packets of sweets were given away, how many people were there at the carnival?

Women	Men	Child
5x11 = 55 u		2x11 = 22 u
4x5 = 20 u	7x5 = 35 u	22 u

	Women	Men	Child
Number	20 u	35 u	22 u
Value	2	3	4
Total Value	40 u	105 u	88 u

Fraction of the people who were adults
= 1 - ²₇
= ⁵₇

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 sweets given away
= 20 u x 2 + 35 u x 3 + 22 u x 4
= 40 u + 105 u + 88 u
= 233 u

233 u = 932

1 u = 932 ÷ 233 = 4

Number of people at the carnival
= 55 u + 22 u
= 77 u
= 77 x 4
= 308

Answer(s): 308