At a school carnival, each boy received 4 packets of lollipops and each girl received 6 packets of lollipops. Each accompanying adult received 8 packets of lollipops. ²₉ 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 2110 packets of lollipops were given away, how many people were there at the carnival?

Boys	Girls	Adults
7x8 = 56 u		2x8 = 16 u
3x7 = 21 u	5x7 = 35 u	16 u

	Boys	Girls	Adults
Number	21 u	35 u	16 u
Value	4	6	8
Total Value	84 u	210 u	128 u

Fraction of the people who were children
= 1 - ²₉
= ⁷₉

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 8 and 7 is 56. 

Number of packets of lollipops given away
= 21 u x 4 + 35 u x 6 + 16 u x 8
= 84 u + 210 u + 128 u
= 422 u

422 u = 2110

1 u = 2110 ÷ 422 = 5

Number of people at the carnival
= 56 u + 16 u
= 72 u
= 72 x 5
= 360

Answer(s): 360