Math Problem

[PooyaH]

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Dr. Hagwood recieved a 25% reduction in his income tax rate, which was 66 2/3% (or same thing as as 2/3). By what percent did his after-tax income increase?

 

[Mstoothlady2012]

nvm I have to double check my answer

 

[Mstoothlady2012]

The first sentence is really confusing. Dr Hagwood got 25% reduction of 66 2/3% or just simply 25% reduction?

Depending on which is true I think the answer is either 75% or 50% respectively.

 

[PooyaH]

The first sentence is really confusing. Dr Hagwood got 25% reduction of 66 2/3% or just simply 25% reduction?

Depending on which is true I think the answer is either 75% or 50% respectively.

Yeah it is confusing! The answer is 50% but I don't know how to get there!

 

[PooyaH]

Nvm...I got it!

so his income-tax was 66 2/3% which is the same thing as 2/3.
So let's say if his income was $60 (just picked the number) his taxe would be 60 (2/3) = $40, leaving him with $20 income.
Now his tax has reduced by 25% or 1/4, so his new tax rate would be:
(3/4) (2/3) = 1/2, so now he pays 60 (1/2) = $30 taxes, which leaves him with $30 income. Now his income has increased by $10. And $10 is 50% of $20!!!

I hope there's a shortcut!

 

[HumanElement]

let y = tax
let x = income

y = 2/3yx
x=1.5
thus 1.5 -1 = .5
therefore it's 50%

Dr. Hagwood recieved a 25% reduction in his income tax rate, which was 66 2/3% (or same thing as as 2/3). By what percent did his after-tax income increase?