40% of the people are performers for a concert and the rest are spectators. 60% of the spectators are children and there are 270 less adult spectators than child spectators. How many child spectators must join so that 84% of the people are child spectators?
|
Performers |
Spectators |
|
2x5 |
3x5 |
|
|
Adults |
Children |
|
|
2x3 |
3x3 |
Before |
10 u |
6 u |
9 u |
Change |
|
|
+ ? |
After |
4x4 = 16 u |
21x4 = 84 u |
40% =
40100 =
25 60% =
60100 =
35 84% =
84100 =
2125The 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 = 270
1 u = 270 ÷ 3 = 90
If some child spectators join, the total number of adult spectators and performers remains unchanged.
Number of child spectators who must join so that 84% of the people are child spectators
= 84 u - 9 u
= 75 u
= 75 x 90
= 6750
Answer(s): 6750