At a school carnival, each woman received 5 packets of mochi balls and each man received 7 packets of mochi balls. Each accompanying child received 9 packets of mochi balls. ⁴₉ 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 2476 packets of mochi balls were given away, how many people were there at the carnival?

Women	Men	Child
5x9 = 45 u		4x9 = 36 u
2x5 = 10 u	7x5 = 35 u	36 u

	Women	Men	Child
Number	10 u	35 u	36 u
Value	5	7	9
Total Value	50 u	245 u	324 u

Fraction of the people who were adults
= 1 - ⁴₉
= ⁵₉

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 mochi balls given away
= 10 u x 5 + 35 u x 7 + 36 u x 9
= 50 u + 245 u + 324 u
= 619 u

619 u = 2476

1 u = 2476 ÷ 619 = 4

Number of people at the carnival
= 45 u + 36 u
= 81 u
= 81 x 4
= 324

Answer(s): 324