40% of the people are performers for a concert and the rest are spectators. 70% of the spectators are adults and there are 1800 less child spectators than adult spectators. How many adult spectators must join so that 71% of the people are adult spectators?
|
Performers |
Spectators |
|
2x10 |
3x10 |
|
|
Children |
Adults |
|
|
3x3 |
7x3 |
Before |
20 u |
9 u |
21 u |
Change |
|
|
+ ? |
After |
29x1 = 29 u |
71x1 = 71 u |
40% =
40100 =
25 70% =
70100 =
710 71% =
71100 =
71100The 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 = 1800
1 u = 1800 ÷ 12 = 150
If some adult spectators join, the total number of child spectators and performers remains unchanged.
Number of adult spectators who must join so that 71% of the people are adult spectators
= 71 u - 21 u
= 50 u
= 50 x 150
= 7500
Answer(s): 7500