At an event held at the stadium, 25% of the audience were adults. The female audience was made up of 40% of the adults and 80% of the children. There were 306 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 |
3 u |
4 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
0.4 u |
0.6 u |
2.4 u |
0.6 u |
|
Change |
+ ? |
|
+ ? |
After |
|
3.6 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
25% =
25100 =
14Number 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
= 80% x 3 u
=
80100 x 3 u
= 2.4 u
Number of boys
= 3 u - 2.4 u
= 0.6 u
Number of more girls than boys
= 2.4 u - 0.6 u
= 1.8 u
1.8 u = 306
1 u = 306 ÷ 1.8 = 170
Number of children
= 3 u
= 3 x 170
= 510
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
3.6 u = 4 p
Number of men and children
= 0.6 u + 3 u
= 3.6 u
= 3.6 x 170
= 612
4 p = 3.6 u
4 p = 612
1 p = 612 ÷ 4 = 153
Number of women in the end
= 1 p
= 153
Number of women at first
= 0.4 u
= 0.4 x 170
= 68
Number of women who joined before the event ended
= 153 - 68
= 85
Answers: (a) 510; (b) 85