At a school carnival, each woman received 3 packets of mini cupcakes and each man received 4 packets of mini cupcakes. Each accompanying child received 6 packets of mini cupcakes. ²₇ 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 : 5. Given that only 642 packets of mini cupcakes were given away, how many people were there at the carnival?

Women	Men	Child
5x7 = 35 u		2x7 = 14 u
2x5 = 10 u	5x5 = 25 u	14 u

	Women	Men	Child
Number	10 u	25 u	14 u
Value	3	4	6
Total Value	30 u	100 u	84 u

Fraction of the people who were adults
= 1 - ²₇
= ⁵₇

The number of adults is the combined repeated identity. Make the number of adults the same.  LCM of 7 and 5 is 35. 

Number of packets of mini cupcakes given away
= 10 u x 3 + 25 u x 4 + 14 u x 6
= 30 u + 100 u + 84 u
= 214 u

214 u = 642

1 u = 642 ÷ 214 = 3

Number of people at the carnival
= 35 u + 14 u
= 49 u
= 49 x 3
= 147

Answer(s): 147