At a school carnival, each girl received 3 packets of chocolate bars and each boy received 5 packets of chocolate bars. Each accompanying adult received 6 packets of chocolate bars. ⁴₉ of the people at the school carnival were adults. The ratio of the number of girls to the number of boys at the carnival was 2 : 7. Given that only 3368 packets of chocolate bars were given away, how many people were there at the carnival?

Girls	Boys	Adults
5x9 = 45 u		4x9 = 36 u
2x5 = 10 u	7x5 = 35 u	36 u

	Girls	Boys	Adults
Number	10 u	35 u	36 u
Value	3	5	6
Total Value	30 u	175 u	216 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 9 and 5 is 45. 

Number of packets of chocolate bars given away
= 10 u x 3 + 35 u x 5 + 36 u x 6
= 30 u + 175 u + 216 u
= 421 u

421 u = 3368

1 u = 3368 ÷ 421 = 8

Number of people at the carnival
= 45 u + 36 u
= 81 u
= 81 x 8
= 648

Answer(s): 648