At a school carnival, each boy received 2 packets of mini cupcakes and each girl received 3 packets of mini cupcakes. Each accompanying adult received 5 packets of mini cupcakes. 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 3 : 5. Given that only 1295 packets of mini cupcakes were given away, how many people were there at the carnival?

Boys	Girls	Adults
5x8 = 40 u		2x8 = 16 u
3x5 = 15 u	5x5 = 25 u	16 u

	Boys	Girls	Adults
Number	15 u	25 u	16 u
Value	2	3	5
Total Value	30 u	75 u	80 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 8 and 5 is 40. 

Number of packets of mini cupcakes given away
= 15 u x 2 + 25 u x 3 + 16 u x 5
= 30 u + 75 u + 80 u
= 185 u

185 u = 1295

1 u = 1295 ÷ 185 = 7

Number of people at the carnival
= 40 u + 16 u
= 56 u
= 56 x 7
= 392

Answer(s): 392