At a school carnival, each woman received 5 packets of mini cupcakes and each man received 6 packets of mini cupcakes. Each accompanying child received 7 packets of mini cupcakes. 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 : 5. Given that only 609 packets of mini cupcakes were given away, how many people were there at the carnival?

Women	Men	Child
4x2 = 8 u		3x2 = 6 u
3x1 = 3 u	5x1 = 5 u	6 u

	Women	Men	Child
Number	3 u	5 u	6 u
Value	5	6	7
Total Value	15 u	30 u	42 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 8 and 4 is 8. 

Number of packets of mini cupcakes given away
= 3 u x 5 + 5 u x 6 + 6 u x 7
= 15 u + 30 u + 42 u
= 87 u

87 u = 609

1 u = 609 ÷ 87 = 7

Number of people at the carnival
= 8 u + 6 u
= 14 u
= 14 x 7
= 98

Answer(s): 98