At a school carnival, each man received 3 packets of mini cupcakes and each woman received 4 packets of mini cupcakes. Each accompanying child received 6 packets of mini cupcakes. ⁴₉ of the people at the school carnival were child. The ratio of the number of men to the number of women at the carnival was 5 : 8. Given that only 2188 packets of mini cupcakes were given away, how many people were there at the carnival?

Men	Women	Child
5x13 = 65 u		4x13 = 52 u
5x5 = 25 u	8x5 = 40 u	52 u

	Men	Women	Child
Number	25 u	40 u	52 u
Value	3	4	6
Total Value	75 u	160 u	312 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 13 and 5 is 65. 

Number of packets of mini cupcakes given away
= 25 u x 3 + 40 u x 4 + 52 u x 6
= 75 u + 160 u + 312 u
= 547 u

547 u = 2188

1 u = 2188 ÷ 547 = 4

Number of people at the carnival
= 65 u + 52 u
= 117 u
= 117 x 4
= 468

Answer(s): 468