At a school carnival, each boy received 2 packets of lollipops and each girl received 4 packets of lollipops. Each accompanying adult received 5 packets of lollipops. ²₉ 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 3 : 7. Given that only 1690 packets of lollipops were given away, how many people were there at the carnival?

Boys	Girls	Adults
7x10 = 70 u		2x10 = 20 u
3x7 = 21 u	7x7 = 49 u	20 u

	Boys	Girls	Adults
Number	21 u	49 u	20 u
Value	2	4	5
Total Value	42 u	196 u	100 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 10 and 7 is 70. 

Number of packets of lollipops given away
= 21 u x 2 + 49 u x 4 + 20 u x 5
= 42 u + 196 u + 100 u
= 338 u

338 u = 1690

1 u = 1690 ÷ 338 = 5

Number of people at the carnival
= 70 u + 20 u
= 90 u
= 90 x 5
= 450

Answer(s): 450