At a school carnival, each woman received 4 packets of chocolate bars and each man received 6 packets of chocolate bars. Each accompanying child received 7 packets of chocolate bars. 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 5 : 7. Given that only 4522 packets of chocolate bars were given away, how many people were there at the carnival?

Women	Men	Child
5x12 = 60 u		4x12 = 48 u
5x5 = 25 u	7x5 = 35 u	48 u

	Women	Men	Child
Number	25 u	35 u	48 u
Value	4	6	7
Total Value	100 u	210 u	336 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 12 and 5 is 60. 

Number of packets of chocolate bars given away
= 25 u x 4 + 35 u x 6 + 48 u x 7
= 100 u + 210 u + 336 u
= 646 u

646 u = 4522

1 u = 4522 ÷ 646 = 7

Number of people at the carnival
= 60 u + 48 u
= 108 u
= 108 x 7
= 756

Answer(s): 756