At a school carnival, each boy received 3 packets of lollipops and each girl received 4 packets of lollipops. Each accompanying adult received 6 packets of lollipops. ²₇ 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 : 7. Given that only 834 packets of lollipops were given away, how many people were there at the carnival?

Boys	Girls	Adults
5x9 = 45 u		2x9 = 18 u
2x5 = 10 u	7x5 = 35 u	18 u

	Boys	Girls	Adults
Number	10 u	35 u	18 u
Value	3	4	6
Total Value	30 u	140 u	108 u

Fraction of the people who were children
= 1 - ²₇
= ⁵₇

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 9 and 5 is 45. 

Number of packets of lollipops given away
= 10 u x 3 + 35 u x 4 + 18 u x 6
= 30 u + 140 u + 108 u
= 278 u

278 u = 834

1 u = 834 ÷ 278 = 3

Number of people at the carnival
= 45 u + 18 u
= 63 u
= 63 x 3
= 189

Answer(s): 189