At the concert hall were some adults.
12 of the number of locals was equal to 3 times the number of tourists. When another 56 tourists entered and 54 locals left, the ratio of the number of locals to the number of tourists become 5 : 3. Find the number of tourists at the concert hall at first.
|
Make p the same (1)x3 = (3) |
Locals (1) |
Tourists (2) |
Make p the same (2)x5 = (4) |
Before |
18 u |
6 u |
1 u |
5 u |
Change |
- 162 |
- 54 |
+ 56 |
+ 280 |
After |
15 p |
5 p |
3 p |
15 p |
12 of the locals = 3 times of the tourists
1x32x3 of the locals =
3x11x1 of the tourists
Make the numerators the same. LCM of 1 and 3 is 3.
36 of the locals =
31 of the tourists
Locals : Tourists = 6 : 1
Make p the same.
(3) = (4)
18 u - 162 = 5 u + 280
18 u - 5 u = 280 + 162
13 u = 442
1 u = 442 ÷ 13 = 34
Number of tourists at the concert hall at first
= 1 u
= 34
Answer(s): 34