At a school carnival, each boy received 5 packets of candy canes and each girl received 6 packets of candy canes. Each accompanying adult received 7 packets of candy canes. ²₅ 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 2177 packets of candy canes were given away, how many people were there at the carnival?

Boys	Girls	Adults
3x10 = 30 u		2x10 = 20 u
3x3 = 9 u	7x3 = 21 u	20 u

	Boys	Girls	Adults
Number	9 u	21 u	20 u
Value	5	6	7
Total Value	45 u	126 u	140 u

Fraction of the people who were children
= 1 - ²₅
= ³₅

The number of children is the combined repeated identity. Make the number of children the same.  LCM of 10 and 3 is 30. 

Number of packets of candy canes given away
= 9 u x 5 + 21 u x 6 + 20 u x 7
= 45 u + 126 u + 140 u
= 311 u

311 u = 2177

1 u = 2177 ÷ 311 = 7

Number of people at the carnival
= 30 u + 20 u
= 50 u
= 50 x 7
= 350

Answer(s): 350