At a school carnival, each boy received 3 packets of candy canes and each girl received 4 packets of candy canes. Each accompanying adult received 6 packets of candy canes.
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 5 : 7. Given that only 2012 packets of candy canes were given away, how many people were there at the carnival?
Boys |
Girls |
Adults |
5x12 = 60 u |
4x12 = 48 u |
5x5 = 25 u |
7x5 = 35 u |
48 u |
|
Boys |
Girls |
Adults |
Number |
25 u |
35 u |
48 u |
Value |
3 |
4 |
6 |
Total Value |
75 u |
140 u |
288 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 12 and 5 is 60.
Number of packets of candy canes given away
= 25 u x 3 + 35 u x 4 + 48 u x 6
= 75 u + 140 u + 288 u
= 503 u
503 u = 2012
1 u = 2012 ÷ 503 = 4
Number of people at the carnival
= 60 u + 48 u
= 108 u
= 108 x 4
= 432
Answer(s): 432