At a school carnival, each woman received 3 packets of mochi balls and each man received 4 packets of mochi balls. Each accompanying child received 6 packets of mochi balls. 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 2 : 5. Given that only 152 packets of mochi balls were given away, how many people were there at the carnival?

Women	Men	Child
7x1 = 7 u		2x1 = 2 u
2x1 = 2 u	5x1 = 5 u	2 u

	Women	Men	Child
Number	2 u	5 u	2 u
Value	3	4	6
Total Value	6 u	20 u	12 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 7 and 7 is 7. 

Number of packets of mochi balls given away
= 2 u x 3 + 5 u x 4 + 2 u x 6
= 6 u + 20 u + 12 u
= 38 u

38 u = 152

1 u = 152 ÷ 38 = 4

Number of people at the carnival
= 7 u + 2 u
= 9 u
= 9 x 4
= 36

Answer(s): 36