At an event held at the stadium, 20% of the audience were adults. The female audience was made up of 20% of the adults and 70% of the children. There were 336 more girls than boys.
- How many children went to the stadium in total?
- Some women joined before the event ended, after which 10% 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 |
0.2 u |
0.8 u |
2.8 u |
1.2 u |
|
Change |
+ ? |
|
+ ? |
After |
|
4.8 u |
|
Comparison in the end |
1 p |
9 p |
10 p |
(a)
20% =
20100 =
15Number of women
= 20% x 1 u
=
20100 x 1 u
= 0.2 u
Number of men
= 1 u - 0.2 u
= 0.8 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 = 336
1 u = 336 ÷ 1.6 = 210
Number of children
= 4 u
= 4 x 210
= 840
(b)
10% =
10100 =
110The total number of men and children in the end is repeated.
4.8 u = 9 p
Number of men and children
= 0.8 u + 4 u
= 4.8 u
= 4.8 x 210
= 1008
9 p = 4.8 u
9 p = 1008
1 p = 1008 ÷ 9 = 112
Number of women in the end
= 1 p
= 112
Number of women at first
= 0.2 u
= 0.2 x 210
= 42
Number of women who joined before the event ended
= 112 - 42
= 70
Answers: (a) 840; (b) 70