At a school carnival, each man received 3 packets of mini cupcakes and each woman received 4 packets of mini cupcakes. Each accompanying child received 6 packets of mini cupcakes.
29 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 2 : 7. Given that only 3114 packets of mini cupcakes were given away, how many people were there at the carnival?
Men |
Women |
Child |
7x9 = 63 u |
2x9 = 18 u |
2x7 = 14 u |
7x7 = 49 u |
18 u |
|
Men |
Women |
Child |
Number |
14 u |
49 u |
18 u |
Value |
3 |
4 |
6 |
Total Value |
42 u |
196 u |
108 u |
Fraction of the people who were adults
= 1 -
29=
79 The number of adults is the combined repeated identity. Make the number of adults the same. LCM of 9 and 7 is 63.
Number of packets of mini cupcakes given away
= 14 u x 3 + 49 u x 4 + 18 u x 6
= 42 u + 196 u + 108 u
= 346 u
346 u = 3114
1 u = 3114 ÷ 346 = 9
Number of people at the carnival
= 63 u + 18 u
= 81 u
= 81 x 9
= 729
Answer(s): 729