30% of the people are performers for a concert and the rest are spectators. 80% of the spectators are adults and there are 840 more adult spectators than child spectators. How many adult spectators must leave so that 45% of the people are adult spectators?
|
Performers |
Spectators |
|
3x5 |
7x5 |
|
|
Children |
Adults |
|
|
1x7 |
4x7 |
Before |
15 u |
7 u |
28 u |
Change |
|
|
- ? |
After |
11x2 = 22 u |
9x2 = 18 u |
30% =
30100 =
310 80% =
80100 =
45 45% =
45100 =
920The 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 more adult spectators than child spectators at first
= 28 u - 7 u
= 21 u
21 u = 840
1 u = 840 ÷ 21 = 40
If some adult spectators leave, the total number of child spectators and performers remains unchanged.
Number of adult spectators who must leave so that 45% of the people are adult spectators
= 28 u - 18 u
= 10 u
= 10 x 40
= 400
Answer(s): 400