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Akash from Surat asks, "There were 200 fishes in an aquarium, 99% of which were red. How many red fishes must be removed to make the percentage of red fishes 98%?"
Hi Akash, let's see if we can set up a solution for this one.
First of all, 99% of 200 is 198 red fish. (Because 200 x 0.99 is 198).
If we remove x red fish from the tank, we have 198 - x red fish left out of 200 - x total.
Thus, the equation we need is (198 - x)/(200 - x) = 0.98.
198 - x = 0.98(200 - x)
198 - x = 196 - 0.98x
2 = 0.02x
x = 100 red fish removed.
Let's check our answer. If we remove 100 fish, and they're all red, we'll have 198 - 100 = 98 red fish, and a total of 200 - 100 = 100 fish.
Sure enough, 98 out of 100 is 98%.
It's tempting to think that if 198 fish is 99%, then 196 must be 98%, but that reasoning forgets that we aren't just decreasing the number of red fish; we're also decreasing the total number of fish!
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