At a school carnival, each boy received 5 packets of chocolate bars and each girl received 6 packets of chocolate bars. Each accompanying adult received 7 packets of chocolate bars. ²₅ 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 5 : 8. Given that only 3208 packets of chocolate bars were given away, how many people were there at the carnival?

Boys	Girls	Adults
3x13 = 39 u		2x13 = 26 u
5x3 = 15 u	8x3 = 24 u	26 u

	Boys	Girls	Adults
Number	15 u	24 u	26 u
Value	5	6	7
Total Value	75 u	144 u	182 u

Fraction of the people who were children
= 1 - ²₅
= ³₅

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 13 and 3 is 39. 

Number of packets of chocolate bars given away
= 15 u x 5 + 24 u x 6 + 26 u x 7
= 75 u + 144 u + 182 u
= 401 u

401 u = 3208

1 u = 3208 ÷ 401 = 8

Number of people at the carnival
= 39 u + 26 u
= 65 u
= 65 x 8
= 520

Answer(s): 520