At a school carnival, each girl received 3 packets of caramel apples and each boy received 4 packets of caramel apples. Each accompanying adult received 5 packets of caramel apples. ²₉ 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 4 : 5. Given that only 2512 packets of caramel apples were given away, how many people were there at the carnival?

Girls	Boys	Adults
7x9 = 63 u		2x9 = 18 u
4x7 = 28 u	5x7 = 35 u	18 u

	Girls	Boys	Adults
Number	28 u	35 u	18 u
Value	3	4	5
Total Value	84 u	140 u	90 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 9 and 7 is 63. 

Number of packets of caramel apples given away
= 28 u x 3 + 35 u x 4 + 18 u x 5
= 84 u + 140 u + 90 u
= 314 u

314 u = 2512

1 u = 2512 ÷ 314 = 8

Number of people at the carnival
= 63 u + 18 u
= 81 u
= 81 x 8
= 648

Answer(s): 648