To determine how much extra Mauro has to pay in federal taxes after winning the lottery, we will compute his federal tax before and after winning the lottery and find the difference.
First, we calculate Mauro's federal tax before winning the lottery:
1. Annual income before winning the lottery: \[tex]$34,500.
2. Federal tax calculation before winning the lottery:
\[
\text{Tax before} = \$[/tex]4386.25 + 0.25 \times (\[tex]$34500 - \$[/tex]31850)
\]
[tex]\[
\text{Tax before} = \$4386.25 + 0.25 \times \$2650
\][/tex]
[tex]\[
\text{Tax before} = \$4386.25 + \$662.50
\][/tex]
[tex]\[
\text{Tax before} = \$5048.75
\][/tex]
Next, we calculate Mauro's federal tax after winning the lottery:
1. Annual income after winning the lottery: \[tex]$34,500 + \$[/tex]349,700 = \[tex]$384,200.
2. Federal tax calculation after winning the lottery using the chart formula:
\[
\text{Tax after} = \$[/tex]101469.25 + 0.35 \times (\[tex]$384200 - \$[/tex]349700)
\]
[tex]\[
\text{Tax after} = \$101469.25 + 0.35 \times \$34500
\][/tex]
[tex]\[
\text{Tax after} = \$101469.25 + \$12075
\][/tex]
[tex]\[
\text{Tax after} = \$113544.25
\][/tex]
To find the extra federal tax Mauro has to pay because he won the lottery, we subtract his tax before winning the lottery from his tax after winning the lottery:
[tex]\[
\text{Extra tax} = \text{Tax after} - \text{Tax before}
\][/tex]
[tex]\[
\text{Extra tax} = \$113544.25 - \$5048.75
\][/tex]
[tex]\[
\text{Extra tax} = \$108495.50
\][/tex]
Therefore, the best answer from the choices provided is:
a. \[tex]$5,048.75
b. \$[/tex]336,100.50
c. \[tex]$341,149.25
d. \$[/tex]676,260.76
So, the correct answer is a. \$5048.75.
