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.
25 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 5 : 7. Given that only 784 packets of mini cupcakes were given away, how many people were there at the carnival?
Men |
Women |
Child |
3x4 = 12 u |
2x4 = 8 u |
5x1 = 5 u |
7x1 = 7 u |
8 u |
|
Men |
Women |
Child |
Number |
5 u |
7 u |
8 u |
Value |
3 |
5 |
6 |
Total Value |
15 u |
35 u |
48 u |
Fraction of the people who were adults
= 1 -
25=
35 The number of adults is the combined repeated identity. Make the number of adults the same. LCM of 12 and 3 is 12.
Number of packets of mini cupcakes given away
= 5 u x 3 + 7 u x 5 + 8 u x 6
= 15 u + 35 u + 48 u
= 98 u
98 u = 784
1 u = 784 ÷ 98 = 8
Number of people at the carnival
= 12 u + 8 u
= 20 u
= 20 x 8
= 160
Answer(s): 160