At an event held at the stadium, 40% of the audience were adults. The female audience was made up of 10% of the adults and 70% of the children. There were 156 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 |
|
2 u |
3 u |
5 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
0.2 u |
1.8 u |
2.1 u |
0.9 u |
|
Change |
+ ? |
|
+ ? |
After |
|
4.8 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
40% =
40100 =
25Number of women
= 10% x 2 u
=
10100 x 2 u
= 0.2 u
Number of men
= 2 u - 0.2 u
= 1.8 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 = 156
1 u = 156 ÷ 1.2 = 130
Number of children
= 3 u
= 3 x 130
= 390
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
4.8 u = 4 p
Number of men and children
= 1.8 u + 3 u
= 4.8 u
= 4.8 x 130
= 624
4 p = 4.8 u
4 p = 624
1 p = 624 ÷ 4 = 156
Number of women in the end
= 1 p
= 156
Number of women at first
= 0.2 u
= 0.2 x 130
= 26
Number of women who joined before the event ended
= 156 - 26
= 130
Answers: (a) 390; (b) 130