Question

Fedor paid $14,761.50 in Income Tax last year. Use the following Total Tax / Annual Income relationship to determine Fedor's annual income last year. Total Tax = Annual Income x $0.10, $952.50 + (Annual Income - 9,525) $0.12, $4,453.50 + (Annual Income - 38,700) < $0.22, $14,089.50 + (Annual Income - 82,500) < $0.24, $32,089.50 + (Annual Income - 157,500) < $0.32, $45,689.50 + (Annual Income - 200,000) < $0.35, $150,689.50 + (Annual Income - 500,000) < $0.37, if $0 S Annual Income s $9,525 if $9,525 < Annual Income s $38.700 if $38,700 < Annual Income < $82,500 if $82,500 < Annual Income s $157,500 if $157,500 < Annual Income < $200,000 if $200,000 < Annual Income < $500,000 if $500,000 < Annual Income

Answer 1

Fedor's annual income last year was $85,300

Here, we want to use the list of relationships between total tax and annual income to determine the annual income last year

What we will do here is to look at the value of the income tax

Afterwards, we can check the range in which it falls

From the different ranges given, we can see that the value $14,761.50 falls on the fourth range

The relationship is given by;

`14,089.5\text{ + (annual income - 82,500) }*\text{ 0.24}`

We simply equate this to the value of the income tax given

That would be;

`\begin{gathered} 14,761.5\text{ = 14,089.5 + (annual income - 82,500) }*\text{ 0.24} \\ \\ 14,761.5-14,089.5\text{ = (A.I - 82,500) }*\text{ 0.24} \\ \\ 672\text{ = (A.I - 82,500) }*\text{ 0.24} \\ (672)/(0.24)\text{ = (A.I-82,500)} \\ \\ 2800\text{ = A.I - 82,500} \\ \\ A\mathrm{}I\text{ = 82,500 + 2,800} \\ \\ A\mathrm{}I\text{ = \$85,300} \end{gathered}`