At an event held at the stadium, 25% of the audience were adults. The female audience was made up of 10% of the adults and 70% of the children. There were 180 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 |
3 u |
4 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
0.1 u |
0.9 u |
2.1 u |
0.9 u |
|
Change |
+ ? |
|
+ ? |
After |
|
3.9 u |
|
Comparison in the end |
1 p |
3 p |
4 p |
(a)
25% =
25100 =
14Number of women
= 10% x 1 u
=
10100 x 1 u
= 0.1 u
Number of men
= 1 u - 0.1 u
= 0.9 u
Number of girls
= 70% x 3 u
=
70100 x 3 u
= 2.1 u
Number of boys
= 3 u - 2.1 u
= 0.9 u
Number of more girls than boys
= 2.1 u - 0.9 u
= 1.2 u
1.2 u = 180
1 u = 180 ÷ 1.2 = 150
Number of children
= 3 u
= 3 x 150
= 450
(b)
25% =
25100 =
14The total number of men and children in the end is repeated.
3.9 u = 3 p
Number of men and children
= 0.9 u + 3 u
= 3.9 u
= 3.9 x 150
= 585
3 p = 3.9 u
3 p = 585
1 p = 585 ÷ 3 = 195
Number of women in the end
= 1 p
= 195
Number of women at first
= 0.1 u
= 0.1 x 150
= 15
Number of women who joined before the event ended
= 195 - 15
= 180
Answers: (a) 450; (b) 180