At a school carnival, each woman received 4 packets of candy canes and each man received 6 packets of candy canes. Each accompanying child received 7 packets of candy canes. ⁴₉ 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 : 7. Given that only 1794 packets of candy canes were given away, how many people were there at the carnival?

Women	Men	Child
5x11 = 55 u		4x11 = 44 u
4x5 = 20 u	7x5 = 35 u	44 u

	Women	Men	Child
Number	20 u	35 u	44 u
Value	4	6	7
Total Value	80 u	210 u	308 u

Fraction of the people who were adults
= 1 - ⁴₉
= ⁵₉

The number of adults is the combined repeated identity. Make the number of adults the same.  LCM of 11 and 5 is 55. 

Number of packets of candy canes given away
= 20 u x 4 + 35 u x 6 + 44 u x 7
= 80 u + 210 u + 308 u
= 598 u

598 u = 1794

1 u = 1794 ÷ 598 = 3

Number of people at the carnival
= 55 u + 44 u
= 99 u
= 99 x 3
= 297

Answer(s): 297