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 70% of the children. There were 72 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 |
2.1 u |
0.9 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
= 70% x 3 u
=
70100 x 3 u
= 2.1 u
Number of boys
= 3 u - 2.1 u
= 0.9 u
Number of more girls than boys
= 2.1 u - 0.9 u
= 1.2 u
1.2 u = 72
1 u = 72 ÷ 1.2 = 60
Number of people
= 5 u
= 5 x 60
= 300
(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 60
= 252
9 p = 4.2 u
9 p = 252
1 p = 252 ÷ 9 = 28
Number of women in the end
= 1 p
= 28
Number of women at first
= 0.8 u
= 0.8 x 60
= 48
Number of women who left before the event ended
= 48 - 28
= 20
Answers: (a) 300; (b) 20