At a school carnival, each woman received 2 packets of chocolate bars and each man received 3 packets of chocolate bars. Each accompanying child received 4 packets of chocolate bars. 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 : 5. Given that only 889 packets of chocolate bars were given away, how many people were there at the carnival?

Women	Men	Child
3x8 = 24 u		2x8 = 16 u
3x3 = 9 u	5x3 = 15 u	16 u

	Women	Men	Child
Number	9 u	15 u	16 u
Value	2	3	4
Total Value	18 u	45 u	64 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 8 and 3 is 24. 

Number of packets of chocolate bars given away
= 9 u x 2 + 15 u x 3 + 16 u x 4
= 18 u + 45 u + 64 u
= 127 u

127 u = 889

1 u = 889 ÷ 127 = 7

Number of people at the carnival
= 24 u + 16 u
= 40 u
= 40 x 7
= 280

Answer(s): 280