40% of the people are performers for a concert and the rest are spectators. 80% of the spectators are children and there are 450 less adult spectators than child spectators. How many child spectators must join so that 87% of the people are child spectators?
|
Performers |
Spectators |
|
2x5 |
3x5 |
|
|
Adults |
Children |
|
|
1x3 |
4x3 |
Before |
10 u |
3 u |
12 u |
Change |
|
|
+ ? |
After |
13x1 = 13 u |
87x1 = 87 u |
40% =
40100 =
25 80% =
80100 =
45 87% =
87100 =
87100The 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
= 12 u - 3 u
= 9 u
9 u = 450
1 u = 450 ÷ 9 = 50
If some child spectators join, the total number of adult spectators and performers remains unchanged.
Number of child spectators who must join so that 87% of the people are child spectators
= 87 u - 12 u
= 75 u
= 75 x 50
= 3750
Answer(s): 3750