At an event held at the stadium, 70% of the audience were adults. The female audience was made up of 30% of the adults and 70% of the children. There were 108 less boys than girls.
- How many people went to the stadium in total?
- Some women left before the event ended, after which 10% of the remaining people at the stadium were women. How many women left the stadium before it ended?
|
Adults |
Children |
Total |
|
7 u |
3 u |
10 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
2.1 u |
4.9 u |
2.1 u |
0.9 u |
|
Change |
- ? |
|
- ? |
After |
|
7.9 u |
|
Comparison in the end |
1 p |
9 p |
10 p |
(a)
70% =
70100 =
710Number of women
= 30% x 7 u
=
30100 x 7 u
= 2.1 u
Number of men
= 7 u - 2.1 u
= 4.9 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 = 108
1 u = 108 ÷ 1.2 = 90
Number of people
= 10 u
= 10 x 90
= 900
(b)
10% =
10100 =
110The total number of men and children in the end is repeated.
7.9 u = 9 p
Number of men and children
= 4.9 u + 3 u
= 7.9 u
= 7.9 x 90
= 711
9 p = 7.9 u
9 p = 711
1 p = 711 ÷ 9 = 79
Number of women in the end
= 1 p
= 79
Number of women at first
= 2.1 u
= 2.1 x 90
= 189
Number of women who left before the event ended
= 189 - 79
= 110
Answers: (a) 900; (b) 110