At a school carnival, each woman received 3 packets of lollipops and each man received 4 packets of lollipops. Each accompanying child received 5 packets of lollipops. 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 3 : 8. Given that only 1275 packets of lollipops were given away, how many people were there at the carnival?

Women	Men	Child
5x11 = 55 u		4x11 = 44 u
3x5 = 15 u	8x5 = 40 u	44 u

	Women	Men	Child
Number	15 u	40 u	44 u
Value	3	4	5
Total Value	45 u	160 u	220 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 lollipops given away
= 15 u x 3 + 40 u x 4 + 44 u x 5
= 45 u + 160 u + 220 u
= 425 u

425 u = 1275

1 u = 1275 ÷ 425 = 3

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

Answer(s): 297