Problem:
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?
Answer Choices:
A. $28000
B. $32000
C. $35000
D. $42000
E. $56000
Solution:
If Kristin's annual income is x≥28,000 dollars, then
100p⋅28,000+100p+2⋅(x−28,000)=100p+0.25⋅x.
Multiplying by 100 and expanding yields
28,000p+px+2x−28,000p−56,000=px+0.25x.
So, 1.75x=47x=56,000 and x=32,000.
Answer: B.
The problems on this page are the property of the MAA's American Mathematics Competitions