At an event held at the stadium, 20% of the audience were adults. The female audience was made up of 20% of the adults and 80% of the children. There were 312 more girls than boys.
- How many children went to the stadium in total?
- Some women joined before the event ended, after which 25% 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 |
0.2 u |
0.8 u |
3.2 u |
0.8 u |
|
Change |
+ ? |
|
+ ? |
After |
|
4.8 u |
|
Comparison in the end |
1 p |
3 p |
4 p |
(a)
20% =
20100 =
15Number of women
= 20% x 1 u
=
20100 x 1 u
= 0.2 u
Number of men
= 1 u - 0.2 u
= 0.8 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 = 312
1 u = 312 ÷ 2.4 = 130
Number of children
= 4 u
= 4 x 130
= 520
(b)
25% =
25100 =
14The total number of men and children in the end is repeated.
4.8 u = 3 p
Number of men and children
= 0.8 u + 4 u
= 4.8 u
= 4.8 x 130
= 624
3 p = 4.8 u
3 p = 624
1 p = 624 ÷ 3 = 208
Number of women in the end
= 1 p
= 208
Number of women at first
= 0.2 u
= 0.2 x 130
= 26
Number of women who joined before the event ended
= 208 - 26
= 182
Answers: (a) 520; (b) 182