30% of the people are performers for a concert and the rest are spectators. 80% of the spectators are parents and there are 3780 less child spectators than parent spectators. How many parent spectators must join so that 78% of the people are parent spectators?
|
Performers |
Spectators |
|
3x5 |
7x5 |
|
|
Children |
Parents |
|
|
1x7 |
4x7 |
Before |
15 u |
7 u |
28 u |
Change |
|
|
+ ? |
After |
11x2 = 22 u |
39x2 = 78 u |
30% =
30100 =
310 80% =
80100 =
45 78% =
78100 =
3950The 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 child spectators than parent spectators at first
= 28 u - 7 u
= 21 u
21 u = 3780
1 u = 3780 ÷ 21 = 180
If some parent spectators join, the total number of child spectators and performers remains unchanged.
Number of parent spectators who must join so that 78% of the people are parent spectators
= 78 u - 28 u
= 50 u
= 50 x 180
= 9000
Answer(s): 9000