Question 1165001
first 2500 of income is not taxed.
next 5000 of income is taxed at 2%
all income over 7500 is taxed at 5%.


total tax is 365.



let x = amount of money taxed at 0%.
let y = amount of money taxed at 2%.
let z = amount of money taxed at 5%.


your equation becomes 0 * x + .02 * y + .05 * z = 365


since you are paying more than 0 tax, then x = 2500.


since .02 * 5000 = 100, and you still have more taxes to pay, then y = 5000


since the total tax is 365 and you paid 100 already, then you still owe 265 in taxes.


this will be at the 5% rate.


to find out what the income is you set up the equation of .05 * z = 265
solve for z to get z = 265 / .05 = 5300.


you have x = 2500, y = 5000, and z = 5300.


your total income is 2500 + 5000 + 5300 = 12,800.


the first 2500 of this is not taxed, so the remainder is 12,800 - 2500 = 10,300 with tax on the 2500 = 0.


the next 5000 of this is taxed at 2%, so the remainder is 10300 - 5000 = 5300 with tax on the 5000 = 100.


the last 5300 of this is taxed at 5%, so the tax is .05 * 5300 = 265.


total tax is 0 + 100 + 265 = 365.


this confirms the solution is correct.


your solution is that his income is 12,800.