At a school carnival, each woman received 2 packets of caramel apples and each man received 4 packets of caramel apples. Each accompanying child received 6 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 2 : 7. Given that only 476 packets of caramel apples were given away, how many people were there at the carnival?

Women	Men	Child
3x3 = 9 u		2x3 = 6 u
2x1 = 2 u	7x1 = 7 u	6 u

	Women	Men	Child
Number	2 u	7 u	6 u
Value	2	4	6
Total Value	4 u	28 u	36 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 9 and 3 is 9. 

Number of packets of caramel apples given away
= 2 u x 2 + 7 u x 4 + 6 u x 6
= 4 u + 28 u + 36 u
= 68 u

68 u = 476

1 u = 476 ÷ 68 = 7

Number of people at the carnival
= 9 u + 6 u
= 15 u
= 15 x 7
= 105

Answer(s): 105