At a school carnival, each man received 5 packets of mini cupcakes and each woman received 6 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 : 7. Given that only 1971 packets of mini cupcakes were given away, how many people were there at the carnival?

Men	Women	Child
4x5 = 20 u		3x5 = 15 u
3x2 = 6 u	7x2 = 14 u	15 u

	Men	Women	Child
Number	6 u	14 u	15 u
Value	5	6	7
Total Value	30 u	84 u	105 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 10 and 4 is 20. 

Number of packets of mini cupcakes given away
= 6 u x 5 + 14 u x 6 + 15 u x 7
= 30 u + 84 u + 105 u
= 219 u

219 u = 1971

1 u = 1971 ÷ 219 = 9

Number of people at the carnival
= 20 u + 15 u
= 35 u
= 35 x 9
= 315

Answer(s): 315