At a school carnival, each woman received 3 packets of mochi balls and each man received 5 packets of mochi balls. Each accompanying child received 6 packets of mochi balls.
25 of the people at the school carnival were child. The ratio of the number of women to the number of men at the carnival was 3 : 5. Given that only 1782 packets of mochi balls were given away, how many people were there at the carnival?
Women |
Men |
Child |
3x8 = 24 u |
2x8 = 16 u |
3x3 = 9 u |
5x3 = 15 u |
16 u |
|
Women |
Men |
Child |
Number |
9 u |
15 u |
16 u |
Value |
3 |
5 |
6 |
Total Value |
27 u |
75 u |
96 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 8 and 3 is 24.
Number of packets of mochi balls given away
= 9 u x 3 + 15 u x 5 + 16 u x 6
= 27 u + 75 u + 96 u
= 198 u
198 u = 1782
1 u = 1782 ÷ 198 = 9
Number of people at the carnival
= 24 u + 16 u
= 40 u
= 40 x 9
= 360
Answer(s): 360