At an event held at the stadium, 20% of the audience were adults. The female audience was made up of 10% of the adults and 70% of the children. There were 256 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 |
4 u |
5 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
0.1 u |
0.9 u |
2.8 u |
1.2 u |
|
Change |
+ ? |
|
+ ? |
After |
|
4.9 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
20% =
20100 =
15Number 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 4 u
=
70100 x 4 u
= 2.8 u
Number of boys
= 4 u - 2.8 u
= 1.2 u
Number of more girls than boys
= 2.8 u - 1.2 u
= 1.6 u
1.6 u = 256
1 u = 256 ÷ 1.6 = 160
Number of children
= 4 u
= 4 x 160
= 640
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
4.9 u = 4 p
Number of men and children
= 0.9 u + 4 u
= 4.9 u
= 4.9 x 160
= 784
4 p = 4.9 u
4 p = 784
1 p = 784 ÷ 4 = 196
Number of women in the end
= 1 p
= 196
Number of women at first
= 0.1 u
= 0.1 x 160
= 16
Number of women who joined before the event ended
= 196 - 16
= 180
Answers: (a) 640; (b) 180