At a school carnival, each man received 3 packets of mochi balls and each woman received 5 packets of mochi balls. Each accompanying child received 6 packets of mochi balls.
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 2 : 5. Given that only 1938 packets of mochi balls were given away, how many people were there at the carnival?
Men |
Women |
Child |
5x7 = 35 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 u |
28 u |
|
Men |
Women |
Child |
Number |
10 u |
25 u |
28 u |
Value |
3 |
5 |
6 |
Total Value |
30 u |
125 u |
168 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 7 and 5 is 35.
Number of packets of mochi balls given away
= 10 u x 3 + 25 u x 5 + 28 u x 6
= 30 u + 125 u + 168 u
= 323 u
323 u = 1938
1 u = 1938 ÷ 323 = 6
Number of people at the carnival
= 35 u + 28 u
= 63 u
= 63 x 6
= 378
Answer(s): 378