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The state income tax where Kristin lives is levied at the rate of p%

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The state income tax where Kristin lives is levied at the rate of p%  [#permalink]

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New post 18 Mar 2019, 02:17
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Difficulty:

  65% (hard)

Question Stats:

56% (02:46) correct 44% (03:19) wrong based on 34 sessions

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The state income tax where Kristin lives is levied at the rate of p% of the first $28000 of annual income plus (p + 2)% of any amount above $28000. Kristin noticed that the state income tax she paid amounted to (p + 0.25)% of her annual income. What was her annual income?


(A) $28000
(B) $32000
(C) $35000
(D) $42000
(E) $56000

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The state income tax where Kristin lives is levied at the rate of p%  [#permalink]

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New post 18 Mar 2019, 02:44
Bunuel wrote:
The state income tax where Kristin lives is levied at the rate of p% of the first $28000 of annual income plus (p + 2)% of any amount above $28000. Kristin noticed that the state income tax she paid amounted to (p + 0.25)% of her annual income. What was her annual income?


(A) $28000
(B) $32000
(C) $35000
(D) $42000
(E) $56000


Given
A(p+.25)/100=28000p/{100+(p+2)*(A-28000)/ 100.

solve for A we get

$(p+.25)A=28000p+Ap+2A-28000p-56000$

$.25A=2A-56000$

$32000
IMO B
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Re: The state income tax where Kristin lives is levied at the rate of p%  [#permalink]

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New post 14 May 2019, 19:05
Archit3110 wrote:
Bunuel wrote:
The state income tax where Kristin lives is levied at the rate of p% of the first $28000 of annual income plus (p + 2)% of any amount above $28000. Kristin noticed that the state income tax she paid amounted to (p + 0.25)% of her annual income. What was her annual income?


(A) $28000
(B) $32000
(C) $35000
(D) $42000
(E) $56000


Given
A(p+.25)/100=28000p/{100+(p+2)*(A-28000)/ 100.

solve for A we get

$(p+.25)A=28000p+Ap+2A-28000p-56000$

$.25A=2A-56000$

$32000
IMO B


I understand this method. But I feel there has to be a much elegant way to solve this than having to create such a complex algebraic equation.
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Re: The state income tax where Kristin lives is levied at the rate of p%   [#permalink] 14 May 2019, 19:05
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The state income tax where Kristin lives is levied at the rate of p%

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