At an event held at the stadium, 30% of the audience were adults. The female audience was made up of 10% of the adults and 80% of the children. There were 756 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 |
|
3 u |
7 u |
10 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
0.3 u |
2.7 u |
5.6 u |
1.4 u |
|
Change |
+ ? |
|
+ ? |
After |
|
9.7 u |
|
Comparison in the end |
1 p |
9 p |
10 p |
(a)
30% =
30100 =
310Number of women
= 10% x 3 u
=
10100 x 3 u
= 0.3 u
Number of men
= 3 u - 0.3 u
= 2.7 u
Number of girls
= 80% x 7 u
=
80100 x 7 u
= 5.6 u
Number of boys
= 7 u - 5.6 u
= 1.4 u
Number of more girls than boys
= 5.6 u - 1.4 u
= 4.2 u
4.2 u = 756
1 u = 756 ÷ 4.2 = 180
Number of children
= 7 u
= 7 x 180
= 1260
(b)
10% =
10100 =
110The total number of men and children in the end is repeated.
9.7 u = 9 p
Number of men and children
= 2.7 u + 7 u
= 9.7 u
= 9.7 x 180
= 1746
9 p = 9.7 u
9 p = 1746
1 p = 1746 ÷ 9 = 194
Number of women in the end
= 1 p
= 194
Number of women at first
= 0.3 u
= 0.3 x 180
= 54
Number of women who joined before the event ended
= 194 - 54
= 140
Answers: (a) 1260; (b) 140