At an event held at the stadium, 20% of the audience were adults. The female audience was made up of 30% of the adults and 80% of the children. There were 576 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 |
0.3 u |
0.7 u |
3.2 u |
0.8 u |
|
Change |
+ ? |
|
+ ? |
After |
|
4.7 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
20% =
20100 =
15Number of women
= 30% x 1 u
=
30100 x 1 u
= 0.3 u
Number of men
= 1 u - 0.3 u
= 0.7 u
Number of girls
= 80% x 4 u
=
80100 x 4 u
= 3.2 u
Number of boys
= 4 u - 3.2 u
= 0.8 u
Number of more girls than boys
= 3.2 u - 0.8 u
= 2.4 u
2.4 u = 576
1 u = 576 ÷ 2.4 = 240
Number of children
= 4 u
= 4 x 240
= 960
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
4.7 u = 4 p
Number of men and children
= 0.7 u + 4 u
= 4.7 u
= 4.7 x 240
= 1128
4 p = 4.7 u
4 p = 1128
1 p = 1128 ÷ 4 = 282
Number of women in the end
= 1 p
= 282
Number of women at first
= 0.3 u
= 0.3 x 240
= 72
Number of women who joined before the event ended
= 282 - 72
= 210
Answers: (a) 960; (b) 210