### Brain Teasers

# Tax

Math
Math brain teasers require computations to solve.

The local city leaders have just placed a 13% tax on hotel rooms. This is on top of a 2% sales tax for the country and a 10% luxury tax. A room now costs $100 per night. How much would it cost without the tax?

### Answer

$80. The $100 includes the $80 plus the 25% tax.Hide Answer Show Answer

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## Comments

it would be nice if the derivation were included in the solution for those who need to see it. SO, here it is... where X = base cost of the room, X + .1X + .02X + .13x = 100 --> 1.25X = 100 --> X = 100/1.25 = 80

i put almost the exact thing on there, but i guess the editors erased it...

i didnt get it

Around here, they would apply the tax to the price with the other taxes already included. I got a different answer.

I agree Gizz. The taxes would be cumulative. The answer is $78.87 to the nearest cent. Thus:

$78.87x1.02x1.1x1.13=$100.

Interesting to note the order in which the taxes are applied does not affect the final price but it does affect who gets what in the breakup.

$78.87x1.02x1.1x1.13=$100.

Interesting to note the order in which the taxes are applied does not affect the final price but it does affect who gets what in the breakup.

To me the wording is a bit unclear. It seems to be written as 'A new tax is put upon hotel rooms. this is on top of tax a and tax b. what is the cost without tax?' Is referring to the new tax or cumulative tax? Either way, I got the same numbers as above. Just an odd choice of wording!

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