At a school carnival, each boy received 5 packets of sweets and each girl received 7 packets of sweets. Each accompanying adult received 9 packets of sweets. ²₇ of the people at the school carnival were adults. The ratio of the number of boys to the number of girls at the carnival was 3 : 7. Given that only 900 packets of sweets were given away, how many people were there at the carnival?

Boys	Girls	Adults
5x2 = 10 u		2x2 = 4 u
3x1 = 3 u	7x1 = 7 u	4 u

	Boys	Girls	Adults
Number	3 u	7 u	4 u
Value	5	7	9
Total Value	15 u	49 u	36 u

Fraction of the people who were children
= 1 - ²₇
= ⁵₇

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 10 and 5 is 10. 

Number of packets of sweets given away
= 3 u x 5 + 7 u x 7 + 4 u x 9
= 15 u + 49 u + 36 u
= 100 u

100 u = 900

1 u = 900 ÷ 100 = 9

Number of people at the carnival
= 10 u + 4 u
= 14 u
= 14 x 9
= 126

Answer(s): 126