At a school carnival, each woman received 2 packets of lollipops and each man received 3 packets of lollipops. Each accompanying child received 4 packets of lollipops. 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 2 : 7. Given that only 1576 packets of lollipops were given away, how many people were there at the carnival?

Women	Men	Child
5x9 = 45 u		2x9 = 18 u
2x5 = 10 u	7x5 = 35 u	18 u

	Women	Men	Child
Number	10 u	35 u	18 u
Value	2	3	4
Total Value	20 u	105 u	72 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 9 and 5 is 45. 

Number of packets of lollipops given away
= 10 u x 2 + 35 u x 3 + 18 u x 4
= 20 u + 105 u + 72 u
= 197 u

197 u = 1576

1 u = 1576 ÷ 197 = 8

Number of people at the carnival
= 45 u + 18 u
= 63 u
= 63 x 8
= 504

Answer(s): 504