20% of the people are performers for a concert and the rest are spectators. 80% of the spectators are adults and there are 2100 more adults spectators than children spectators. How many adult spectators must join so that 90% 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 adults spectators than children spectators at first
= 16 u - 4 u
= 12 u
12 u = 2100
1 u = 2100 ÷ 12 = 175
Number of performers and children spectators
= 9 u
= 9 x 175
= 1575
|
Performers and children spectators |
Adult spectators
|
Before |
9 u (1575) |
16 u |
Change |
|
+ ? |
After |
1 p |
9 p |
90% people =
90100 people =
910 people
Performers and children spectators : Adults = 1 : 9
The total number of performers and children spectators remains the same. The total number of performers and children spectators is the unchanged quantity.
1 p = 1575
Numbers of adult spectators at first
= 16 u
= 16 x 175
= 2800
Number of adult spectators in the end
= 9 x 1575
= 14175
Numbers of adult spectators that must join
= 14175 - 2800
= 11375
Answer: 11375