25% of the people are performers for a concert and the rest are spectators. 70% of the spectators are adults and there are 2160 less child spectators than adult spectators. How many adult spectators must join so that 62% of the people are adult spectators?
|
Performers |
Spectators |
|
1x10 |
3x10 |
|
|
Children |
Adults |
|
|
3x3 |
7x3 |
Before |
10 u |
9 u |
21 u |
Change |
|
|
+ ? |
After |
19x1 = 19 u |
31x1 = 31 u |
25% =
25100 =
14 70% =
70100 =
710 62% =
62100 =
3150The total number of spectators at first is repeated. Make the total number of spectators the same. LCM of 3 and 10 is 30.
Number of less child spectators than adult spectators at first
= 21 u - 9 u
= 12 u
12 u = 2160
1 u = 2160 ÷ 12 = 180
If some adult spectators join, the total number of child spectators and performers remains unchanged.
Number of adult spectators who must join so that 62% of the people are adult spectators
= 31 u - 21 u
= 10 u
= 10 x 180
= 1800
Answer(s): 1800