At a school carnival, each boy received 3 packets of mini cupcakes and each girl received 4 packets of mini cupcakes. Each accompanying adult received 5 packets of mini cupcakes. ⁴₉ 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 : 5. Given that only 2160 packets of mini cupcakes were given away, how many people were there at the carnival?

Boys	Girls	Adults
5x7 = 35 u		4x7 = 28 u
2x5 = 10 u	5x5 = 25 u	28 u

	Boys	Girls	Adults
Number	10 u	25 u	28 u
Value	3	4	5
Total Value	30 u	100 u	140 u

Fraction of the people who were children
= 1 - ⁴₉
= ⁵₉

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 7 and 5 is 35. 

Number of packets of mini cupcakes given away
= 10 u x 3 + 25 u x 4 + 28 u x 5
= 30 u + 100 u + 140 u
= 270 u

270 u = 2160

1 u = 2160 ÷ 270 = 8

Number of people at the carnival
= 35 u + 28 u
= 63 u
= 63 x 8
= 504

Answer(s): 504