At an event held at the stadium, 30% of the audience were adults. The female audience was made up of 30% of the adults and 70% of the children. There were 560 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 |
|
3 u |
7 u |
10 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
0.9 u |
2.1 u |
4.9 u |
2.1 u |
|
Change |
+ ? |
|
+ ? |
After |
|
9.1 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
30% =
30100 =
310Number of women
= 30% x 3 u
=
30100 x 3 u
= 0.9 u
Number of men
= 3 u - 0.9 u
= 2.1 u
Number of girls
= 70% x 7 u
=
70100 x 7 u
= 4.9 u
Number of boys
= 7 u - 4.9 u
= 2.1 u
Number of more girls than boys
= 4.9 u - 2.1 u
= 2.8 u
2.8 u = 560
1 u = 560 ÷ 2.8 = 200
Number of children
= 7 u
= 7 x 200
= 1400
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
9.1 u = 4 p
Number of men and children
= 2.1 u + 7 u
= 9.1 u
= 9.1 x 200
= 1820
4 p = 9.1 u
4 p = 1820
1 p = 1820 ÷ 4 = 455
Number of women in the end
= 1 p
= 455
Number of women at first
= 0.9 u
= 0.9 x 200
= 180
Number of women who joined before the event ended
= 455 - 180
= 275
Answers: (a) 1400; (b) 275