At a school carnival, each girl received 5 packets of caramel apples and each boy received 7 packets of caramel apples. Each accompanying adult received 9 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 2 : 7. Given that only 5750 packets of caramel apples were given away, how many people were there at the carnival?

Girls	Boys	Adults
7x9 = 63 u		2x9 = 18 u
2x7 = 14 u	7x7 = 49 u	18 u

	Girls	Boys	Adults
Number	14 u	49 u	18 u
Value	5	7	9
Total Value	70 u	343 u	162 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
= 14 u x 5 + 49 u x 7 + 18 u x 9
= 70 u + 343 u + 162 u
= 575 u

575 u = 5750

1 u = 5750 ÷ 575 = 10

Number of people at the carnival
= 63 u + 18 u
= 81 u
= 81 x 10
= 810

Answer(s): 810