At an event held at the stadium, 60% of the audience were adults. The female audience was made up of 40% of the adults and 80% of the children. There were 144 less boys than girls.
- How many people went to the stadium in total?
- Some women left before the event ended, after which 20% of the remaining people at the stadium were women. How many women left the stadium before it ended?
|
Adults |
Children |
Total |
|
3 u |
2 u |
5 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
1.2 u |
1.8 u |
1.6 u |
0.4 u |
|
Change |
- ? |
|
- ? |
After |
|
3.8 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
60% =
60100 =
35Number of women
= 40% x 3 u
=
40100 x 3 u
= 1.2 u
Number of men
= 3 u - 1.2 u
= 1.8 u
Number of girls
= 80% x 2 u
=
80100 x 2 u
= 1.6 u
Number of boys
= 2 u - 1.6 u
= 0.4 u
Number of more girls than boys
= 1.6 u - 0.4 u
= 1.2 u
1.2 u = 144
1 u = 144 ÷ 1.2 = 120
Number of people
= 5 u
= 5 x 120
= 600
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
3.8 u = 4 p
Number of men and children
= 1.8 u + 2 u
= 3.8 u
= 3.8 x 120
= 456
4 p = 3.8 u
4 p = 456
1 p = 456 ÷ 4 = 114
Number of women in the end
= 1 p
= 114
Number of women at first
= 1.2 u
= 1.2 x 120
= 144
Number of women who left before the event ended
= 144 - 114
= 30
Answers: (a) 600; (b) 30