At a school carnival, each boy received 5 packets of sweets and each girl received 6 packets of sweets. Each accompanying adult received 7 packets of sweets. 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 : 5. Given that only 741 packets of sweets were given away, how many people were there at the carnival?

Boys	Girls	Adults
3x8 = 24 u		2x8 = 16 u
3x3 = 9 u	5x3 = 15 u	16 u

	Boys	Girls	Adults
Number	9 u	15 u	16 u
Value	5	6	7
Total Value	45 u	90 u	112 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 8 and 3 is 24. 

Number of packets of sweets given away
= 9 u x 5 + 15 u x 6 + 16 u x 7
= 45 u + 90 u + 112 u
= 247 u

247 u = 741

1 u = 741 ÷ 247 = 3

Number of people at the carnival
= 24 u + 16 u
= 40 u
= 40 x 3
= 120

Answer(s): 120