At a school carnival, each girl received 5 packets of mochi balls and each boy received 7 packets of mochi balls. Each accompanying adult received 9 packets of mochi balls. ³₇ of the people at the school carnival were adults. The ratio of the number of girls to the number of boys at the carnival was 5 : 7. Given that only 775 packets of mochi balls were given away, how many people were there at the carnival?

Girls	Boys	Adults
4x3 = 12 u		3x3 = 9 u
5x1 = 5 u	7x1 = 7 u	9 u

	Girls	Boys	Adults
Number	5 u	7 u	9 u
Value	5	7	9
Total Value	25 u	49 u	81 u

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

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 12 and 4 is 12. 

Number of packets of mochi balls given away
= 5 u x 5 + 7 u x 7 + 9 u x 9
= 25 u + 49 u + 81 u
= 155 u

155 u = 775

1 u = 775 ÷ 155 = 5

Number of people at the carnival
= 12 u + 9 u
= 21 u
= 21 x 5
= 105

Answer(s): 105