At a school carnival, each boy received 3 packets of chocolate bars and each girl received 5 packets of chocolate bars. Each accompanying adult received 7 packets of chocolate bars. ⁴₉ 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 chocolate bars were given away, how many people were there at the carnival?

Boys	Girls	Adults
5x2 = 10 u		4x2 = 8 u
3x1 = 3 u	7x1 = 7 u	8 u

	Boys	Girls	Adults
Number	3 u	7 u	8 u
Value	3	5	7
Total Value	9 u	35 u	56 u

Fraction of the people who were children
= 1 - ⁴₉
= ⁵₉

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 chocolate bars given away
= 3 u x 3 + 7 u x 5 + 8 u x 7
= 9 u + 35 u + 56 u
= 100 u

100 u = 900

1 u = 900 ÷ 100 = 9

Number of people at the carnival
= 10 u + 8 u
= 18 u
= 18 x 9
= 162

Answer(s): 162