At a school carnival, each man received 3 packets of mini cupcakes and each woman received 5 packets of mini cupcakes. Each accompanying child received 6 packets of mini cupcakes.
49 of the people at the school carnival were child. The ratio of the number of men to the number of women at the carnival was 4 : 7. Given that only 1996 packets of mini cupcakes were given away, how many people were there at the carnival?
Men |
Women |
Child |
5x11 = 55 u |
4x11 = 44 u |
4x5 = 20 u |
7x5 = 35 u |
44 u |
|
Men |
Women |
Child |
Number |
20 u |
35 u |
44 u |
Value |
3 |
5 |
6 |
Total Value |
60 u |
175 u |
264 u |
Fraction of the people who were adults
= 1 -
49=
59 The number of adults is the combined repeated identity. Make the number of adults the same. LCM of 11 and 5 is 55.
Number of packets of mini cupcakes given away
= 20 u x 3 + 35 u x 5 + 44 u x 6
= 60 u + 175 u + 264 u
= 499 u
499 u = 1996
1 u = 1996 ÷ 499 = 4
Number of people at the carnival
= 55 u + 44 u
= 99 u
= 99 x 4
= 396
Answer(s): 396