At a school carnival, each woman received 3 packets of caramel apples and each man received 5 packets of caramel apples. Each accompanying child received 7 packets of caramel apples. ²₅ of the people at the school carnival were child. The ratio of the number of women to the number of men at the carnival was 5 : 8. Given that only 2776 packets of caramel apples were given away, how many people were there at the carnival?

Women	Men	Child
3x13 = 39 u		2x13 = 26 u
5x3 = 15 u	8x3 = 24 u	26 u

	Women	Men	Child
Number	15 u	24 u	26 u
Value	3	5	7
Total Value	45 u	120 u	182 u

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

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

Number of packets of caramel apples given away
= 15 u x 3 + 24 u x 5 + 26 u x 7
= 45 u + 120 u + 182 u
= 347 u

347 u = 2776

1 u = 2776 ÷ 347 = 8

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

Answer(s): 520