At a school carnival, each woman received 2 packets of mochi balls and each man received 3 packets of mochi balls. Each accompanying child received 5 packets of mochi balls.
29 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 : 8. Given that only 1920 packets of mochi balls were given away, how many people were there at the carnival?
Women |
Men |
Child |
7x11 = 77 u |
2x11 = 22 u |
3x7 = 21 u |
8x7 = 56 u |
22 u |
|
Women |
Men |
Child |
Number |
21 u |
56 u |
22 u |
Value |
2 |
3 |
5 |
Total Value |
42 u |
168 u |
110 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 11 and 7 is 77.
Number of packets of mochi balls given away
= 21 u x 2 + 56 u x 3 + 22 u x 5
= 42 u + 168 u + 110 u
= 320 u
320 u = 1920
1 u = 1920 ÷ 320 = 6
Number of people at the carnival
= 77 u + 22 u
= 99 u
= 99 x 6
= 594
Answer(s): 594