At the concert hall were some adults.
12 of the number of tourists was equal to 3 times the number of locals. When another 35 locals entered and 50 tourists left, the ratio of the number of tourists to the number of locals become 8 : 3. Find the number of locals at the concert hall at first.
|
Make p the same (1)x3 = (3) |
Tourists (1) |
Locals (2) |
Make p the same (2)x8 = (4) |
Before |
18 u |
6 u |
1 u |
8 u |
Change |
- 150 |
- 50 |
+ 35 |
+ 280 |
After |
24 p |
8 p |
3 p |
24 p |
12 of the tourists = 3 times of the locals
1x32x3 of the tourists =
3x11x1 of the locals
Make the numerators the same. LCM of 1 and 3 is 3.
36 of the tourists =
31 of the locals
Tourists : Locals = 6 : 1
Make p the same.
(3) = (4)
18 u - 150 = 8 u + 280
18 u - 8 u = 280 + 150
10 u = 430
1 u = 430 ÷ 10 = 43
Number of locals at the concert hall at first
= 1 u
= 43
Answer(s): 43