SOLUTION: 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

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.

RELATED QUESTIONS
chenthe income tax to be paid on a MAN's Salary is calculated as follows The first $9600 (answered by Theo)

In Fantasy Island an individual pays 10% tax on gross annual income not exceeding... (answered by Theo)

Dear Sir/Madam, I am confronted with the following problem: "A certain state... (answered by prince_abubu)

Use the table to answer the question that follows. Tax Name Investment Earnings Tax... (answered by Boreal)

(See Week 2 Lecture page �Piecewise-Defined Functions� for a starting point.) Income... (answered by Boreal)

Suppose there are no taxes on the first $14000 of income and any income above $14000 is... (answered by rfer)

In city X, the first $30,000 of someone's annual income are taxed at the rate of 5%,... (answered by math_tutor2020)

In Alabama the state income tax paid is directly proportional to the gross monthly... (answered by stanbon)

(6 pts) A particular state computed income tax, T (in dollars) on a person’s income, x (answered by CubeyThePenguin)