At a school carnival, each man received 5 packets of mini cupcakes and each woman received 6 packets of mini cupcakes. Each accompanying child received 8 packets of mini cupcakes.
27 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 3 : 5. Given that only 1412 packets of mini cupcakes were given away, how many people were there at the carnival?
Men |
Women |
Child |
5x8 = 40 u |
2x8 = 16 u |
3x5 = 15 u |
5x5 = 25 u |
16 u |
|
Men |
Women |
Child |
Number |
15 u |
25 u |
16 u |
Value |
5 |
6 |
8 |
Total Value |
75 u |
150 u |
128 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 8 and 5 is 40.
Number of packets of mini cupcakes given away
= 15 u x 5 + 25 u x 6 + 16 u x 8
= 75 u + 150 u + 128 u
= 353 u
353 u = 1412
1 u = 1412 ÷ 353 = 4
Number of people at the carnival
= 40 u + 16 u
= 56 u
= 56 x 4
= 224
Answer(s): 224