Question 1165001: In a certain state, the first $2500 of SMith's income is not taxed; on the next $5000 of income, the tax is 2%; on all income over $7500, the tax is 5%. If Smith pays a tax of $365, find his income.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
|
|
|
