At an event held at the stadium, 80% of the audience were adults. The female audience was made up of 40% of the adults and 80% of the children. There were 24 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 |
|
4 u |
1 u |
5 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
1.6 u |
2.4 u |
0.8 u |
0.2 u |
|
Change |
- ? |
|
- ? |
After |
|
3.4 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
80% =
80100 =
45Number of women
= 40% x 4 u
=
40100 x 4 u
= 1.6 u
Number of men
= 4 u - 1.6 u
= 2.4 u
Number of girls
= 80% x 1 u
=
80100 x 1 u
= 0.8 u
Number of boys
= 1 u - 0.8 u
= 0.2 u
Number of more girls than boys
= 0.8 u - 0.2 u
= 0.6 u
0.6 u = 24
1 u = 24 ÷ 0.6 = 40
Number of people
= 5 u
= 5 x 40
= 200
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
3.4 u = 4 p
Number of men and children
= 2.4 u + 1 u
= 3.4 u
= 3.4 x 40
= 136
4 p = 3.4 u
4 p = 136
1 p = 136 ÷ 4 = 34
Number of women in the end
= 1 p
= 34
Number of women at first
= 1.6 u
= 1.6 x 40
= 64
Number of women who left before the event ended
= 64 - 34
= 30
Answers: (a) 200; (b) 30