At a school carnival, each girl received 3 packets of chocolate bars and each boy received 4 packets of chocolate bars. Each accompanying adult received 5 packets of chocolate bars. 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 5 : 7. Given that only 3789 packets of chocolate bars were given away, how many people were there at the carnival?

Girls	Boys	Adults
7x12 = 84 u		2x12 = 24 u
5x7 = 35 u	7x7 = 49 u	24 u

	Girls	Boys	Adults
Number	35 u	49 u	24 u
Value	3	4	5
Total Value	105 u	196 u	120 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 12 and 7 is 84. 

Number of packets of chocolate bars given away
= 35 u x 3 + 49 u x 4 + 24 u x 5
= 105 u + 196 u + 120 u
= 421 u

421 u = 3789

1 u = 3789 ÷ 421 = 9

Number of people at the carnival
= 84 u + 24 u
= 108 u
= 108 x 9
= 972

Answer(s): 972