At a school carnival, each girl received 2 packets of mochi balls and each boy received 3 packets of mochi balls. Each accompanying adult received 4 packets of mochi balls.
49 of the people at the school carnival were adults. The ratio of the number of girls to the number of boys at the carnival was 3 : 7. Given that only 590 packets of mochi balls were given away, how many people were there at the carnival?
Girls |
Boys |
Adults |
5x2 = 10 u |
4x2 = 8 u |
3x1 = 3 u |
7x1 = 7 u |
8 u |
|
Girls |
Boys |
Adults |
Number |
3 u |
7 u |
8 u |
Value |
2 |
3 |
4 |
Total Value |
6 u |
21 u |
32 u |
Fraction of the people who were children
= 1 -
49=
59 The number of children is the combined repeated identity. Make the number of children the same. LCM of 10 and 5 is 10.
Number of packets of mochi balls given away
= 3 u x 2 + 7 u x 3 + 8 u x 4
= 6 u + 21 u + 32 u
= 59 u
59 u = 590
1 u = 590 ÷ 59 = 10
Number of people at the carnival
= 10 u + 8 u
= 18 u
= 18 x 10
= 180
Answer(s): 180