30% of the people are performers for a concert and the rest are spectators. 80% of the spectators are children and there are 1050 less adult spectators than child spectators. How many child spectators must join so that 78% of the people are child spectators?
|
Performers |
Spectators |
|
3x5 |
7x5 |
|
|
Adults |
Children |
|
|
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 adult spectators than child spectators at first
= 28 u - 7 u
= 21 u
21 u = 1050
1 u = 1050 ÷ 21 = 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 78% of the people are child spectators
= 78 u - 28 u
= 50 u
= 50 x 50
= 2500
Answer(s): 2500