At an event held at the stadium, 75% of the audience were adults. The female audience was made up of 40% of the adults and 80% of the children. There were 90 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 |
1 u |
4 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
1.2 u |
1.8 u |
0.8 u |
0.2 u |
|
Change |
- ? |
|
- ? |
After |
|
2.8 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
75% =
75100 =
34Number 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 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 = 90
1 u = 90 ÷ 0.6 = 150
Number of people
= 4 u
= 4 x 150
= 600
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
2.8 u = 4 p
Number of men and children
= 1.8 u + 1 u
= 2.8 u
= 2.8 x 150
= 420
4 p = 2.8 u
4 p = 420
1 p = 420 ÷ 4 = 105
Number of women in the end
= 1 p
= 105
Number of women at first
= 1.2 u
= 1.2 x 150
= 180
Number of women who left before the event ended
= 180 - 105
= 75
Answers: (a) 600; (b) 75