Solve Word Problem: 2006 Taxes Based on 33% Bracket

[kuahji]

Every year in the US each working American typically pays in taxes a percentage of his or her earnings (minus the stand deuction). Karen's 2005 taxes were calculated based on the formula T(x)= .22(x-6500). That year the standard deduction was $6,500 & her tax bracket paid 22%. Write the function that will determine her 2006 taxes assuming she receives a raise that places her in a 33% braket.

So I wrote at .33(x-6,500). Seemed simply enough, but I guess maybe it was too simple. The book answer is .33(1.25x-6,500). What I don't understand is where the 1.25 came from.

 

[HallsofIvy]

Every year in the US each working American typically pays in taxes a percentage of his or her earnings (minus the stand deuction). Karen's 2005 taxes were calculated based on the formula T(x)= .22(x-6500). That year the standard deduction was $6,500 & her tax bracket paid 22%. Write the function that will determine her 2006 taxes assuming she receives a raise that places her in a 33% braket.

So I wrote at .33(x-6,500). Seemed simply enough, but I guess maybe it was too simple. The book answer is .33(1.25x-6,500). What I don't understand is where the 1.25 came from.

I don't either unless there was more information than you gave us. The book, giving T(x)= .22(x- 6500) is assuming that 22% is the lowest tax bracket. Being in a higher tax bracket, such as 33%, does not mean you pay 33% of taxable income. You pay the lowest percentage, 22% here, on income lower up to the cut off, then the next percentage, which your book is presuming is 33% on income above that. Did your book say what the cutoff between 22% and 33% is?

 

[kuahji]

Nope, that was the complete problem. No hidden information. I thought it was a bit confusing & incomplete myself.

 

[Rowah]

In my experience there are errata in textbooks, especially math ones. The people that compose the answers do so hurriedly and there is room for error. It could be possible that the answer is simply part of the growing errata that exists in our academic world.