At a school carnival, each woman received 2 packets of candy canes and each man received 4 packets of candy canes. Each accompanying child received 5 packets of candy canes. ³₇ 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 : 7. Given that only 415 packets of candy canes were given away, how many people were there at the carnival?

Women	Men	Child
4x3 = 12 u		3x3 = 9 u
5x1 = 5 u	7x1 = 7 u	9 u

	Women	Men	Child
Number	5 u	7 u	9 u
Value	2	4	5
Total Value	10 u	28 u	45 u

Fraction of the people who were adults
= 1 - ³₇
= ⁴₇

The number of adults is the combined repeated identity. Make the number of adults the same.  LCM of 12 and 4 is 12. 

Number of packets of candy canes given away
= 5 u x 2 + 7 u x 4 + 9 u x 5
= 10 u + 28 u + 45 u
= 83 u

83 u = 415

1 u = 415 ÷ 83 = 5

Number of people at the carnival
= 12 u + 9 u
= 21 u
= 21 x 5
= 105

Answer(s): 105