At an event held at the stadium, 70% of the audience were adults. The female audience was made up of 40% of the adults and 80% of the children. There were 126 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 |
|
7 u |
3 u |
10 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
2.8 u |
4.2 u |
2.4 u |
0.6 u |
|
Change |
- ? |
|
- ? |
After |
|
7.2 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
70% =
70100 =
710Number of women
= 40% x 7 u
=
40100 x 7 u
= 2.8 u
Number of men
= 7 u - 2.8 u
= 4.2 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 = 126
1 u = 126 ÷ 1.8 = 70
Number of people
= 10 u
= 10 x 70
= 700
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
7.2 u = 4 p
Number of men and children
= 4.2 u + 3 u
= 7.2 u
= 7.2 x 70
= 504
4 p = 7.2 u
4 p = 504
1 p = 504 ÷ 4 = 126
Number of women in the end
= 1 p
= 126
Number of women at first
= 2.8 u
= 2.8 x 70
= 196
Number of women who left before the event ended
= 196 - 126
= 70
Answers: (a) 700; (b) 70