At a school carnival, each boy received 2 packets of sweets and each girl received 3 packets of sweets. Each accompanying adult received 5 packets of sweets. ³₇ 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 4 : 7. Given that only 2810 packets of sweets were given away, how many people were there at the carnival?

Boys	Girls	Adults
4x11 = 44 u		3x11 = 33 u
4x4 = 16 u	7x4 = 28 u	33 u

	Boys	Girls	Adults
Number	16 u	28 u	33 u
Value	2	3	5
Total Value	32 u	84 u	165 u

Fraction of the people who were children
= 1 - ³₇
= ⁴₇

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 11 and 4 is 44. 

Number of packets of sweets given away
= 16 u x 2 + 28 u x 3 + 33 u x 5
= 32 u + 84 u + 165 u
= 281 u

281 u = 2810

1 u = 2810 ÷ 281 = 10

Number of people at the carnival
= 44 u + 33 u
= 77 u
= 77 x 10
= 770

Answer(s): 770