At a school carnival, each boy received 2 packets of sweets and each girl received 3 packets of sweets. Each accompanying adult received 4 packets of sweets. 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 5 : 8. Given that only 3024 packets of sweets were given away, how many people were there at the carnival?

Boys	Girls	Adults
5x13 = 65 u		4x13 = 52 u
5x5 = 25 u	8x5 = 40 u	52 u

	Boys	Girls	Adults
Number	25 u	40 u	52 u
Value	2	3	4
Total Value	50 u	120 u	208 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 13 and 5 is 65. 

Number of packets of sweets given away
= 25 u x 2 + 40 u x 3 + 52 u x 4
= 50 u + 120 u + 208 u
= 378 u

378 u = 3024

1 u = 3024 ÷ 378 = 8

Number of people at the carnival
= 65 u + 52 u
= 117 u
= 117 x 8
= 936

Answer(s): 936