25% of the people are performers for a concert and the rest are spectators. 60% of the spectators are children and there are 450 less adult spectators than child spectators. How many child spectators must join so that 89% of the people are child spectators?
|
Performers |
Spectators |
|
1x5 |
3x5 |
|
|
Adults |
Children |
|
|
2x3 |
3x3 |
Before |
5 u |
6 u |
9 u |
Change |
|
|
+ ? |
After |
11x1 = 11 u |
89x1 = 89 u |
25% =
25100 =
14 60% =
60100 =
35 89% =
89100 =
89100The total number of spectators at first is repeated. Make the total number of spectators the same. LCM of 3 and 5 is 15.
Number of less adult spectators than child spectators at first
= 9 u - 6 u
= 3 u
3 u = 450
1 u = 450 ÷ 3 = 150
If some child spectators join, the total number of adult spectators and performers remains unchanged.
Number of child spectators who must join so that 89% of the people are child spectators
= 89 u - 9 u
= 80 u
= 80 x 150
= 12000
Answer(s): 12000