30% of the people are performers for a concert and the rest are spectators. 60% of the spectators are children and there are 560 less parent spectators than child spectators. How many child spectators must join so that 71% of the people are child spectators?
|
Performers |
Spectators |
|
3x5 |
7x5 |
|
|
Parents |
Children |
|
|
2x7 |
3x7 |
Before |
15 u |
14 u |
21 u |
Change |
|
|
+ ? |
After |
29x1 = 29 u |
71x1 = 71 u |
30% =
30100 =
310 60% =
60100 =
35 71% =
71100 =
71100The total number of spectators at first is repeated. Make the total number of spectators the same. LCM of 7 and 5 is 35.
Number of less parent spectators than child spectators at first
= 21 u - 14 u
= 7 u
7 u = 560
1 u = 560 ÷ 7 = 80
If some child spectators join, the total number of parent spectators and performers remains unchanged.
Number of child spectators who must join so that 71% of the people are child spectators
= 71 u - 21 u
= 50 u
= 50 x 80
= 4000
Answer(s): 4000