At a school carnival, each boy received 3 packets of mochi balls and each girl received 4 packets of mochi balls. Each accompanying adult received 5 packets of mochi balls. ⁴₉ of the people at the school carnival were adults. The ratio of the number of boys to the number of girls at the carnival was 3 : 5. Given that only 2440 packets of mochi balls were given away, how many people were there at the carnival?

Boys	Girls	Adults
5x8 = 40 u		4x8 = 32 u
3x5 = 15 u	5x5 = 25 u	32 u

	Boys	Girls	Adults
Number	15 u	25 u	32 u
Value	3	4	5
Total Value	45 u	100 u	160 u

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

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 8 and 5 is 40. 

Number of packets of mochi balls given away
= 15 u x 3 + 25 u x 4 + 32 u x 5
= 45 u + 100 u + 160 u
= 305 u

305 u = 2440

1 u = 2440 ÷ 305 = 8

Number of people at the carnival
= 40 u + 32 u
= 72 u
= 72 x 8
= 576

Answer(s): 576