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 90% 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 10% 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 |
3.6 u |
0.4 u |
|
Change |
+ ? |
|
+ ? |
After |
|
4.7 u |
|
Comparison in the end |
1 p |
9 p |
10 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
= 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 = 576
1 u = 576 ÷ 3.2 = 180
Number of children
= 4 u
= 4 x 180
= 720
(b)
10% =
10100 =
110The total number of men and children in the end is repeated.
4.7 u = 9 p
Number of men and children
= 0.7 u + 4 u
= 4.7 u
= 4.7 x 180
= 846
9 p = 4.7 u
9 p = 846
1 p = 846 ÷ 9 = 94
Number of women in the end
= 1 p
= 94
Number of women at first
= 0.3 u
= 0.3 x 180
= 54
Number of women who joined before the event ended
= 94 - 54
= 40
Answers: (a) 720; (b) 40