A city has just passed an ordinance to control the number of fish in a lake. When the number of fish in a lake increases by 60%, 180 fish must immediately be removed from the lake. When this new number of fish increases by 60%, 180 fish must immediately be removed from the lake again, and so on. If the ordinance is followed, which number will result in the number of fish in the lake remaining constant?
Responses
A 180
B 220
C 260
D 300
E 340
Let's set up the problem algebraically. Let's say the original number of fish in the lake is x.
When the number of fish in the lake increases by 60%, it becomes 1.6x.
Then, 180 fish must be removed, so the new number of fish in the lake is 1.6x - 180.
When this new number of fish increases by 60%, it becomes 1.6(1.6x - 180) = 2.56x - 288.
Then, 180 fish must be removed again, so the new number of fish in the lake is 2.56x - 288 - 180 = 2.56x - 468.
Continuing this pattern, we can set up the equation:
2.56x - 468 - 180 = 2.56x - 648 = 1.6x
Simplifying, we have:
2.56x - 648 = 1.6x
Subtracting 1.6x from both sides, we get:
0.96x = 648
Dividing both sides by 0.96, we find:
x = 675
Therefore, the number of fish in the lake that will result in the number of fish remaining constant is 675.
However, none of the answer choices provided match 675. Therefore, there may be an error in the problem or answer choices.