At a school carnival, each woman received 3 packets of candy canes and each man received 5 packets of candy canes. Each accompanying child received 7 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 3 : 8. Given that only 2135 packets of candy canes were given away, how many people were there at the carnival?

Women	Men	Child
4x11 = 44 u		3x11 = 33 u
3x4 = 12 u	8x4 = 32 u	33 u

	Women	Men	Child
Number	12 u	32 u	33 u
Value	3	5	7
Total Value	36 u	160 u	231 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 11 and 4 is 44. 

Number of packets of candy canes given away
= 12 u x 3 + 32 u x 5 + 33 u x 7
= 36 u + 160 u + 231 u
= 427 u

427 u = 2135

1 u = 2135 ÷ 427 = 5

Number of people at the carnival
= 44 u + 33 u
= 77 u
= 77 x 5
= 385

Answer(s): 385