Question

agnes pays state income tax equal to 3.75% of her federal taxable income. she pays federal income tax equal to 28.4% of her federal taxable income. this year, she paid $15,449.60 in federal income tax. how much did agnes pay in state income tax?
a. $573.36
b. $4,387.69
c. $1,170.04
d. $2,040.00
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Identify federal taxable income

Agnes paid $15,449.60 in federal income tax, which is 28.4% of her federal taxable income. Let \( x \) be her federal taxable income. Then \( 0.284x = 15449.60 \). Solving for \( x \): \( x=\frac{15449.60}{0.284}=54400 \).

Step2: Calculate state income tax

State income tax is 3.75% of federal taxable income. So, state tax \( = 0.0375\times54400 \).
\( 0.0375\times54400 = 2040 \)? Wait, no, wait: Wait, 28.4% of federal taxable income is federal tax. Wait, no, the problem says: "Agnes pays state income tax equal to 3.75% of her federal taxable income. She pays federal income tax equal to 28.4% of her federal taxable income. This year, she paid $15,449.60 in federal income tax. How much did Agnes pay in state income tax?"

So first, find federal taxable income (let's call it FTI). Federal tax = 28.4% of FTI = 0.284 * FTI = 15449.60. So FTI = 15449.60 / 0.284. Let's compute that: 15449.60 ÷ 0.284. Let's do 15449.60 ÷ 0.284: 0.284 × 54400 = 15449.60 (because 54400 × 0.28 = 15232, 54400 × 0.004 = 217.6; 15232 + 217.6 = 15449.6). So FTI is $54,400.

Then state tax is 3.75% of FTI: 0.0375 × 54400. Let's calculate that: 54400 × 0.03 = 1632, 54400 × 0.0075 = 408. So 1632 + 408 = 2040? Wait, but the options are a. $573.36, b. $4,387.69, c. $1,170.04, d. $2,040.00. Oh, so d is $2,040.00. Wait, but let's recheck:

Wait, 3.75% of 54400: 54400 0.0375. Let's compute 54400 3.75 / 100. 54400 3.75 = 54400 (15/4) / 100? No, 3.75% is 3/80 (since 3.75 = 15/4, so 15/4 % = 15/(4100) = 3/80). Wait, 54400 3.75% = 54400 * 0.0375 = 2040. So the state tax is $2,040.00, which is option d.

Wait, but let's check the federal tax calculation again. 28.4% of 54400: 54400 0.284. 54400 0.2 = 10880, 54400 0.08 = 4352, 54400 0.004 = 217.6. Sum: 10880 + 4352 = 15232 + 217.6 = 15449.6, which matches the given federal tax. So then state tax is 3.75% of 54400: 54400 * 0.0375 = 2040. So the answer is d.

Answer:

d. $2,040.00