At an event held at the stadium, 80% of the audience were adults. The female audience was made up of 20% of the adults and 80% of the children. There were 108 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 |
|
4 u |
1 u |
5 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
0.8 u |
3.2 u |
0.8 u |
0.2 u |
|
Change |
- ? |
|
- ? |
After |
|
4.2 u |
|
Comparison in the end |
1 p |
9 p |
10 p |
(a)
80% =
80100 =
45Number of women
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of men
= 4 u - 0.8 u
= 3.2 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 = 108
1 u = 108 ÷ 0.6 = 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.
4.2 u = 9 p
Number of men and children
= 3.2 u + 1 u
= 4.2 u
= 4.2 x 180
= 756
9 p = 4.2 u
9 p = 756
1 p = 756 ÷ 9 = 84
Number of women in the end
= 1 p
= 84
Number of women at first
= 0.8 u
= 0.8 x 180
= 144
Number of women who left before the event ended
= 144 - 84
= 60
Answers: (a) 900; (b) 60