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

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Math Expert
Joined: 02 Sep 2009
Posts: 59728
The state income tax where Kristin lives is levied at the rate of p%  [#permalink]

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18 Mar 2019, 02:17
00:00

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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Joined: 18 Aug 2017
Posts: 5484
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
The state income tax where Kristin lives is levied at the rate of p%  [#permalink]

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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
Intern
Joined: 15 Aug 2018
Posts: 9
Re: The state income tax where Kristin lives is levied at the rate of p%  [#permalink]

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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.
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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