At a school carnival, each man received 4 packets of lollipops and each woman received 5 packets of lollipops. Each accompanying child received 6 packets of lollipops. ³₇ of the people at the school carnival were child. The ratio of the number of men to the number of women at the carnival was 4 : 5. Given that only 2934 packets of lollipops were given away, how many people were there at the carnival?

Men	Women	Child
4x9 = 36 u		3x9 = 27 u
4x4 = 16 u	5x4 = 20 u	27 u

	Men	Women	Child
Number	16 u	20 u	27 u
Value	4	5	6
Total Value	64 u	100 u	162 u

Fraction of the people who were adults
= 1 - ³₇
= ⁴₇

The number of adults is the combined repeated identity. Make the number of adults the same.  LCM of 9 and 4 is 36. 

Number of packets of lollipops given away
= 16 u x 4 + 20 u x 5 + 27 u x 6
= 64 u + 100 u + 162 u
= 326 u

326 u = 2934

1 u = 2934 ÷ 326 = 9

Number of people at the carnival
= 36 u + 27 u
= 63 u
= 63 x 9
= 567

Answer(s): 567