At a school carnival, each girl received 5 packets of chocolate bars and each boy received 6 packets of chocolate bars. Each accompanying adult received 8 packets of chocolate bars. ⁴₉ 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 : 7. Given that only 5296 packets of chocolate bars were given away, how many people were there at the carnival?

Girls	Boys	Adults
5x11 = 55 u		4x11 = 44 u
4x5 = 20 u	7x5 = 35 u	44 u

	Girls	Boys	Adults
Number	20 u	35 u	44 u
Value	5	6	8
Total Value	100 u	210 u	352 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 11 and 5 is 55. 

Number of packets of chocolate bars given away
= 20 u x 5 + 35 u x 6 + 44 u x 8
= 100 u + 210 u + 352 u
= 662 u

662 u = 5296

1 u = 5296 ÷ 662 = 8

Number of people at the carnival
= 55 u + 44 u
= 99 u
= 99 x 8
= 792

Answer(s): 792