There are t tarantulas and r rats in a perspex box in the Australian jungle!
An animal is taken at random from the box.
The probability that the animal is a rat is 3/7.
The animal is put back in the box.
Two more tarantulas and three more rats are put in the box.
Another animal is taken at random from the box.
The probability that the animal is a rat is 6/13.
Find the number of tarantulas and the number of rats that were in the box originally.
Answer:
Let:
R = original number of rats
T = original number of tarantulas
X = Total number at start
R = 3/7 * X
Once new animals are put in:
13 (R + 3)/6 = X + 5
13R + 39 = 6X + 30
13R + 9 = 6X
X = (13R + 9)/6
Substituting back in:
R = 3/7 * (13R + 9)/6
42R = 39R + 27
3R = 27
R = 9
So X = R * 7/3 = 21
Therefore T = 21 – 9 = 12
So there were 9 rats and 12 tarantulas originally.