At a school carnival, each woman received 5 packets of candy canes and each man received 6 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 4 : 5. Given that only 1167 packets of candy canes were given away, how many people were there at the carnival?

Women	Men	Child
4x9 = 36 u		3x9 = 27 u
4x4 = 16 u	5x4 = 20 u	27 u

	Women	Men	Child
Number	16 u	20 u	27 u
Value	5	6	7
Total Value	80 u	120 u	189 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 9 and 4 is 36. 

Number of packets of candy canes given away
= 16 u x 5 + 20 u x 6 + 27 u x 7
= 80 u + 120 u + 189 u
= 389 u

389 u = 1167

1 u = 1167 ÷ 389 = 3

Number of people at the carnival
= 36 u + 27 u
= 63 u
= 63 x 3
= 189

Answer(s): 189