At a school carnival, each woman received 2 packets of mochi balls and each man received 4 packets of mochi balls. Each accompanying child received 6 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 4 : 7. Given that only 1536 packets of mochi balls were given away, how many people were there at the carnival?
Women |
Men |
Child |
7x11 = 77 u |
2x11 = 22 u |
4x7 = 28 u |
7x7 = 49 u |
22 u |
|
Women |
Men |
Child |
Number |
28 u |
49 u |
22 u |
Value |
2 |
4 |
6 |
Total Value |
56 u |
196 u |
132 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
= 28 u x 2 + 49 u x 4 + 22 u x 6
= 56 u + 196 u + 132 u
= 384 u
384 u = 1536
1 u = 1536 ÷ 384 = 4
Number of people at the carnival
= 77 u + 22 u
= 99 u
= 99 x 4
= 396
Answer(s): 396