At a school carnival, each woman received 5 packets of sweets and each man received 7 packets of sweets. Each accompanying child received 8 packets of sweets. ²₉ 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 : 5. Given that only 1587 packets of sweets were given away, how many people were there at the carnival?

Women	Men	Child
7x9 = 63 u		2x9 = 18 u
4x7 = 28 u	5x7 = 35 u	18 u

	Women	Men	Child
Number	28 u	35 u	18 u
Value	5	7	8
Total Value	140 u	245 u	144 u

Fraction of the people who were adults
= 1 - ²₉
= ⁷₉

The number of adults is the combined repeated identity. Make the number of adults the same.  LCM of 9 and 7 is 63. 

Number of packets of sweets given away
= 28 u x 5 + 35 u x 7 + 18 u x 8
= 140 u + 245 u + 144 u
= 529 u

529 u = 1587

1 u = 1587 ÷ 529 = 3

Number of people at the carnival
= 63 u + 18 u
= 81 u
= 81 x 3
= 243

Answer(s): 243