#### Step-by-Step Solution:
1. Calculate the taxable income:
- Start with the gross salary: \[tex]$87,300.
- Subtract the standard deduction: \$[/tex]12,200.
[tex]\[
\text{Taxable Income} = \$87,300 - \$12,200 = \$75,100
\][/tex]
2. Apply the progressive tax rates to the taxable income:
- The first \[tex]$9,700 is taxed at 10%.
- The next \$[/tex]29,775 (\[tex]$39,475 - \$[/tex]9,700) is taxed at 12%.
- The remaining amount up to \[tex]$75,100 between \$[/tex]39,476 and \[tex]$75,100 is taxed at 22%.
3. Breakdown of tax owed in each bracket:
- For the first \$[/tex]9,700:
[tex]\[
\$9,700 \times 10\% = \$970
\][/tex]
- For the next \[tex]$29,775:
\[
\$[/tex]29,775 \times 12\% = \[tex]$3,573
\]
- For the remaining amount up to \$[/tex]75,100:
[tex]\[
(\$75,100 - \$39,475) = \$35,625
\][/tex]
This portion is taxed at 22%:
[tex]\[
\$35,625 \times 22\% = \$7,837.5
\][/tex]
4. Calculate the total tax owed:
Sum up the taxes calculated for each bracket:
[tex]\[
\$970 + \$3,573 + \$7,837.5 = \$12,380.5
\][/tex]
So, the taxable income is \[tex]$75,100, and the federal income tax owed is \$[/tex]12,380.5.
