smc

Question

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?

Accepted Answer

Let A, T be Kristin's annual income and the income tax total, respectively. Notice that align* T &= p%28000 + (p + 2)%(A - 28000) &= [p%28000 + p%(A - 28000)] + 2%(A - 28000) &= p% A + 2%(A - 28000) align* We are also given that T = (p + 0.25)% A = p% A + 0.25% A Thus, p% A + 2%(A - 28000) = p% A + 0.25% A 2%(A - 28000) = 0.25% A Solve for A to obtain A = , 32000.