At an event held at the stadium, 40% of the audience were adults. The female audience was made up of 40% of the adults and 80% of the children. There were 162 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 |
|
2 u |
3 u |
5 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
0.8 u |
1.2 u |
2.4 u |
0.6 u |
|
Change |
- ? |
|
- ? |
After |
|
4.2 u |
|
Comparison in the end |
1 p |
9 p |
10 p |
(a)
40% =
40100 =
25Number of women
= 40% x 2 u
=
40100 x 2 u
= 0.8 u
Number of men
= 2 u - 0.8 u
= 1.2 u
Number of girls
= 80% x 3 u
=
80100 x 3 u
= 2.4 u
Number of boys
= 3 u - 2.4 u
= 0.6 u
Number of more girls than boys
= 2.4 u - 0.6 u
= 1.8 u
1.8 u = 162
1 u = 162 ÷ 1.8 = 90
Number of people
= 5 u
= 5 x 90
= 450
(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
= 1.2 u + 3 u
= 4.2 u
= 4.2 x 90
= 378
9 p = 4.2 u
9 p = 378
1 p = 378 ÷ 9 = 42
Number of women in the end
= 1 p
= 42
Number of women at first
= 0.8 u
= 0.8 x 90
= 72
Number of women who left before the event ended
= 72 - 42
= 30
Answers: (a) 450; (b) 30