At an event held at the stadium, 20% of the audience were adults. The female audience was made up of 40% of the adults and 90% of the children. There were 320 more girls than boys.
- How many children went to the stadium in total?
- Some women joined before the event ended, after which 20% of the remaining people at the stadium were women. How many women joined the stadium before it ended?
|
Adults |
Children |
Total |
|
1 u |
4 u |
5 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
0.4 u |
0.6 u |
3.6 u |
0.4 u |
|
Change |
+ ? |
|
+ ? |
After |
|
4.6 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
20% =
20100 =
15Number of women
= 40% x 1 u
=
40100 x 1 u
= 0.4 u
Number of men
= 1 u - 0.4 u
= 0.6 u
Number of girls
= 90% x 4 u
=
90100 x 4 u
= 3.6 u
Number of boys
= 4 u - 3.6 u
= 0.4 u
Number of more girls than boys
= 3.6 u - 0.4 u
= 3.2 u
3.2 u = 320
1 u = 320 ÷ 3.2 = 100
Number of children
= 4 u
= 4 x 100
= 400
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
4.6 u = 4 p
Number of men and children
= 0.6 u + 4 u
= 4.6 u
= 4.6 x 100
= 460
4 p = 4.6 u
4 p = 460
1 p = 460 ÷ 4 = 115
Number of women in the end
= 1 p
= 115
Number of women at first
= 0.4 u
= 0.4 x 100
= 40
Number of women who joined before the event ended
= 115 - 40
= 75
Answers: (a) 400; (b) 75