## Ask Professor Puzzler

Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!

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!

# Ask Professor Puzzler

Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!**Get a**

*FREE*Pro-Membership!Educators can get a free membership simply by sharing an original lesson plan on our

*Articles for Educators*page!