At a school carnival, each boy received 5 packets of candy canes and each girl received 7 packets of candy canes. Each accompanying adult received 8 packets of candy canes. 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 2 : 5. Given that only 1348 packets of candy canes were given away, how many people were there at the carnival?

Boys	Girls	Adults
5x7 = 35 u		2x7 = 14 u
2x5 = 10 u	5x5 = 25 u	14 u

	Boys	Girls	Adults
Number	10 u	25 u	14 u
Value	5	7	8
Total Value	50 u	175 u	112 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 7 and 5 is 35. 

Number of packets of candy canes given away
= 10 u x 5 + 25 u x 7 + 14 u x 8
= 50 u + 175 u + 112 u
= 337 u

337 u = 1348

1 u = 1348 ÷ 337 = 4

Number of people at the carnival
= 35 u + 14 u
= 49 u
= 49 x 4
= 196

Answer(s): 196