At a school carnival, each woman received 3 packets of mini cupcakes and each man received 5 packets of mini cupcakes. Each accompanying child received 6 packets of mini cupcakes.
27 of the people at the school carnival were child. The ratio of the number of women to the number of men at the carnival was 3 : 7. Given that only 204 packets of mini cupcakes were given away, how many people were there at the carnival?
Women |
Men |
Child |
5x2 = 10 u |
2x2 = 4 u |
3x1 = 3 u |
7x1 = 7 u |
4 u |
|
Women |
Men |
Child |
Number |
3 u |
7 u |
4 u |
Value |
3 |
5 |
6 |
Total Value |
9 u |
35 u |
24 u |
Fraction of the people who were adults
= 1 -
27=
57 The number of adults is the combined repeated identity. Make the number of adults the same. LCM of 10 and 5 is 10.
Number of packets of mini cupcakes given away
= 3 u x 3 + 7 u x 5 + 4 u x 6
= 9 u + 35 u + 24 u
= 68 u
68 u = 204
1 u = 204 ÷ 68 = 3
Number of people at the carnival
= 10 u + 4 u
= 14 u
= 14 x 3
= 42
Answer(s): 42