At a school carnival, each boy received 2 packets of chocolate bars and each girl received 4 packets of chocolate bars. Each accompanying adult received 5 packets of chocolate bars. ²₇ 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 4 : 5. Given that only 1150 packets of chocolate bars were given away, how many people were there at the carnival?

Boys	Girls	Adults
5x9 = 45 u		2x9 = 18 u
4x5 = 20 u	5x5 = 25 u	18 u

	Boys	Girls	Adults
Number	20 u	25 u	18 u
Value	2	4	5
Total Value	40 u	100 u	90 u

Fraction of the people who were children
= 1 - ²₇
= ⁵₇

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
= 20 u x 2 + 25 u x 4 + 18 u x 5
= 40 u + 100 u + 90 u
= 230 u

230 u = 1150

1 u = 1150 ÷ 230 = 5

Number of people at the carnival
= 45 u + 18 u
= 63 u
= 63 x 5
= 315

Answer(s): 315