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: Find federal taxable income

Let \( x \) be federal taxable income. Federal tax is \( 28.4\% \) of \( x \), so \( 0.284x = 15449.60 \). Solve for \( x \): \( x=\frac{15449.60}{0.284} \).
\( x = \frac{15449.60}{0.284}=54400 \)

Step2: Calculate state income tax

State tax is \( 3.75\% \) of \( x \). So state tax \( = 0.0375\times54400 \).
\( 0.0375\times54400 = 2040 \)? Wait, no, wait: Wait, 54400 0.0375: 54400 3.75% = 54400 0.0375 = 2040? Wait, but let's check again. Wait, 15449.60 divided by 0.284: 15449.60 / 0.284. Let's compute that: 0.284 50000 = 14200, 15449.60 - 14200 = 1249.60. 1249.60 / 0.284 = 4400. So total x = 50000 + 4400 = 54400. Then 54400 0.0375: 54400 3/80 = (54400/80)3 = 6803=2040? Wait, but option d is 2040. But wait, maybe I made a mistake. Wait, 3.75% is 3/80? 3.75/100 = 3/80. 54400 3/80 = (54400/80)3 = 680*3=2040. So state tax is $2040.00. Wait, but let's check again. Wait, federal tax is 28.4% of x = 15449.60. So x = 15449.60 / 0.284. Let's do this division: 15449.60 ÷ 0.284. Multiply numerator and denominator by 1000: 15449600 ÷ 284. 284 * 50000 = 14200000. 15449600 - 14200000 = 1249600. 284 * 4400 = 284*4000=1,136,000; 284*400=113,600; total 1,136,000+113,600=1,249,600. So 50000+4400=54400. Then 54400 * 0.0375 = 54400 * 3/80 = 2040. So the state tax is $2040.00, which is option d. Wait, but let's check the options. Option d is $2,040.00. So the answer is d.

Answer:

d. $2,040.00