At a school carnival, each man received 4 packets of mochi balls and each woman received 6 packets of mochi balls. Each accompanying child received 8 packets of mochi balls. ²₉ 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 2 : 5. Given that only 540 packets of mochi balls were given away, how many people were there at the carnival?

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

	Men	Women	Child
Number	2 u	5 u	2 u
Value	4	6	8
Total Value	8 u	30 u	16 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 4 + 5 u x 6 + 2 u x 8
= 8 u + 30 u + 16 u
= 54 u

54 u = 540

1 u = 540 ÷ 54 = 10

Number of people at the carnival
= 7 u + 2 u
= 9 u
= 9 x 10
= 90

Answer(s): 90