At an event held at the stadium, 70% of the audience were adults. The female audience was made up of 20% of the adults and 90% of the children. There were 336 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 |
|
7 u |
3 u |
10 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
1.4 u |
5.6 u |
2.7 u |
0.3 u |
|
Change |
+ ? |
|
+ ? |
After |
|
8.6 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
70% =
70100 =
710Number of women
= 20% x 7 u
=
20100 x 7 u
= 1.4 u
Number of men
= 7 u - 1.4 u
= 5.6 u
Number of girls
= 90% x 3 u
=
90100 x 3 u
= 2.7 u
Number of boys
= 3 u - 2.7 u
= 0.3 u
Number of more girls than boys
= 2.7 u - 0.3 u
= 2.4 u
2.4 u = 336
1 u = 336 ÷ 2.4 = 140
Number of children
= 3 u
= 3 x 140
= 420
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
8.6 u = 4 p
Number of men and children
= 5.6 u + 3 u
= 8.6 u
= 8.6 x 140
= 1204
4 p = 8.6 u
4 p = 1204
1 p = 1204 ÷ 4 = 301
Number of women in the end
= 1 p
= 301
Number of women at first
= 1.4 u
= 1.4 x 140
= 196
Number of women who joined before the event ended
= 301 - 196
= 105
Answers: (a) 420; (b) 105