At a school carnival, each boy received 3 packets of sweets and each girl received 5 packets of sweets. Each accompanying adult received 6 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 : 5. Given that only 2170 packets of sweets were given away, how many people were there at the carnival?

Boys	Girls	Adults
4x9 = 36 u		3x9 = 27 u
4x4 = 16 u	5x4 = 20 u	27 u

	Boys	Girls	Adults
Number	16 u	20 u	27 u
Value	3	5	6
Total Value	48 u	100 u	162 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 9 and 4 is 36. 

Number of packets of sweets given away
= 16 u x 3 + 20 u x 5 + 27 u x 6
= 48 u + 100 u + 162 u
= 310 u

310 u = 2170

1 u = 2170 ÷ 310 = 7

Number of people at the carnival
= 36 u + 27 u
= 63 u
= 63 x 7
= 441

Answer(s): 441