At a school carnival, each man received 4 packets of mini cupcakes and each woman received 5 packets of mini cupcakes. Each accompanying child received 7 packets of mini cupcakes. ³₇ 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 3 : 8. Given that only 4390 packets of mini cupcakes were given away, how many people were there at the carnival?

Men	Women	Child
4x11 = 44 u		3x11 = 33 u
3x4 = 12 u	8x4 = 32 u	33 u

	Men	Women	Child
Number	12 u	32 u	33 u
Value	4	5	7
Total Value	48 u	160 u	231 u

Fraction of the people who were adults
= 1 - ³₇
= ⁴₇

The number of adults is the combined repeated identity. Make the number of adults the same.  LCM of 11 and 4 is 44. 

Number of packets of mini cupcakes given away
= 12 u x 4 + 32 u x 5 + 33 u x 7
= 48 u + 160 u + 231 u
= 439 u

439 u = 4390

1 u = 4390 ÷ 439 = 10

Number of people at the carnival
= 44 u + 33 u
= 77 u
= 77 x 10
= 770

Answer(s): 770