At a school carnival, each girl received 5 packets of candy canes and each boy received 6 packets of candy canes. Each accompanying adult received 7 packets of candy canes.
49 of the people at the school carnival were adults. The ratio of the number of girls to the number of boys at the carnival was 2 : 7. Given that only 3072 packets of candy canes were given away, how many people were there at the carnival?
Girls |
Boys |
Adults |
5x9 = 45 u |
4x9 = 36 u |
2x5 = 10 u |
7x5 = 35 u |
36 u |
|
Girls |
Boys |
Adults |
Number |
10 u |
35 u |
36 u |
Value |
5 |
6 |
7 |
Total Value |
50 u |
210 u |
252 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 9 and 5 is 45.
Number of packets of candy canes given away
= 10 u x 5 + 35 u x 6 + 36 u x 7
= 50 u + 210 u + 252 u
= 512 u
512 u = 3072
1 u = 3072 ÷ 512 = 6
Number of people at the carnival
= 45 u + 36 u
= 81 u
= 81 x 6
= 486
Answer(s): 486