At an event held at the stadium, 60% of the audience were adults. The female audience was made up of 20% of the adults and 90% of the children. There were 288 less boys than girls.
- How many people went to the stadium in total?
- Some women left before the event ended, after which 10% 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 |
0.6 u |
2.4 u |
1.8 u |
0.2 u |
|
Change |
- ? |
|
- ? |
After |
|
4.4 u |
|
Comparison in the end |
1 p |
9 p |
10 p |
(a)
60% =
60100 =
35Number of women
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of men
= 3 u - 0.6 u
= 2.4 u
Number of girls
= 90% x 2 u
=
90100 x 2 u
= 1.8 u
Number of boys
= 2 u - 1.8 u
= 0.2 u
Number of more girls than boys
= 1.8 u - 0.2 u
= 1.6 u
1.6 u = 288
1 u = 288 ÷ 1.6 = 180
Number of people
= 5 u
= 5 x 180
= 900
(b)
10% =
10100 =
110The total number of men and children in the end is repeated.
4.4 u = 9 p
Number of men and children
= 2.4 u + 2 u
= 4.4 u
= 4.4 x 180
= 792
9 p = 4.4 u
9 p = 792
1 p = 792 ÷ 9 = 88
Number of women in the end
= 1 p
= 88
Number of women at first
= 0.6 u
= 0.6 x 180
= 108
Number of women who left before the event ended
= 108 - 88
= 20
Answers: (a) 900; (b) 20