I have a goal of getting exactly $100. But I have to pay a tax of 10%. How much money do I need to get in order to have exactly $100 after paying tax? Explain your answer please.

Explanation:

Let's say you earn x dollars.

You pay 10% tax on that, which means you pay 0.10x dollars.

This would drop to x-0.10x = 0.90x which is the amount earned after tax.

So you pay 10% of what you earn, and keep 90% of the rest.

Set this equal to the target $100 you want and solve for x.

0.90x = 100

x = 100/0.90

x = 111.11

Notice that 10% of this is 0.10*x = 0.10*111.11 = 1.11 when rounding to the nearest penny. So you'll pay $1.11 in tax. Therefore, you'd have x-0.10x = 111.11 - 1.11 = 100 left over. So the answer checks out.

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