At a school carnival, each boy received 5 packets of mochi balls and each girl received 7 packets of mochi balls. Each accompanying adult received 8 packets of mochi balls. ³₇ 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 2 : 7. Given that only 3164 packets of mochi balls were given away, how many people were there at the carnival?

Boys	Girls	Adults
4x9 = 36 u		3x9 = 27 u
2x4 = 8 u	7x4 = 28 u	27 u

	Boys	Girls	Adults
Number	8 u	28 u	27 u
Value	5	7	8
Total Value	40 u	196 u	216 u

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

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

Number of packets of mochi balls given away
= 8 u x 5 + 28 u x 7 + 27 u x 8
= 40 u + 196 u + 216 u
= 452 u

452 u = 3164

1 u = 3164 ÷ 452 = 7

Number of people at the carnival
= 36 u + 27 u
= 63 u
= 63 x 7
= 441

Answer(s): 441