At a school carnival, each boy received 4 packets of candy canes and each girl received 6 packets of candy canes. Each accompanying adult received 8 packets of candy canes. 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 2 : 5. Given that only 828 packets of candy canes were given away, how many people were there at the carnival?

Boys	Girls	Adults
5x7 = 35 u		4x7 = 28 u
2x5 = 10 u	5x5 = 25 u	28 u

	Boys	Girls	Adults
Number	10 u	25 u	28 u
Value	4	6	8
Total Value	40 u	150 u	224 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 7 and 5 is 35. 

Number of packets of candy canes given away
= 10 u x 4 + 25 u x 6 + 28 u x 8
= 40 u + 150 u + 224 u
= 414 u

414 u = 828

1 u = 828 ÷ 414 = 2

Number of people at the carnival
= 35 u + 28 u
= 63 u
= 63 x 2
= 126

Answer(s): 126