20% of the people are performers for a concert and the rest are spectators. 80% of the spectators are adults and there are 2400 more adults spectators than children spectators. How many adult spectators must leave so that 25% of the people in the concert are adult spectators?
Spectators |
Performers |
Total |
4x5 = 20 u |
1x5 = 5 u |
5x5 = 25 u |
Adult spectators |
Children spectators |
|
|
4x4 |
1x4 |
|
|
16 u |
4 u |
5 u |
25 u |
20% =
20100 =
15 Spectators : Performers = 4 : 1
80% =
80100 =
45 Adults : Children = 4 : 1
The number of spectators is the combined repeated identity. Make the number of spectators the same. LCM of 4 and 5 is 20.
Number of more adult spectators than children spectators at first
= 16 u - 4 u
= 12 u
12 u = 2400
1 u = 2400 ÷ 12 = 200
Number of performers and children spectators
= 9 u
= 9 x 200
= 1800
|
Performers and children spectators |
Adult spectators
|
Before |
9 u (1800) |
16 u |
Change |
|
- ? |
After |
3 p |
1 p |
25% people =
25100 people =
14 people
Performers and children spectators : Adults = 3 : 1
The total number of performers and children spectators remains the same. The total number of performers and children spectators is the unchanged quantity.
3 p = 1800
1 p = 1800 ÷ 3 = 600
Numbers of adult spectators at first
= 16 u
= 16 x 200
= 3200
Numbers of adult spectators that must leave
= 3200 - 600
= 2600
Answer: 2600