We know that there exists both provincial tax and surtax in Ontario. The provincial tax brackets and the surtax rates are provided below:

Ontario Tax $2023$ From To Rate

$$0$

$$45,142$

$5\mathrm{.}05\%$

$$49,231$

$$90,287$

$9\mathrm{.}15\%$

$$98,463$

$$150,000$

$11\mathrm{.}16\%$

$$150,000$

$$220,000$

$12\mathrm{.}16\%$

$$220,000$

Infinity

$13\mathrm{.}16\%$

Part A: How much income results in paying $$5,315$ as provincial tax? How much income leads to a $$6,802$ provincial tax?

Part B: Since the presence of surtax makes the tax system unnecessarily complicated, we decide to eliminate it$.$ However, we don$$t want to reduce the amount of tax that the provincial government collects. Using the two thresholds in Part A$,$ as a result of eliminating surtax, how would you change the provincial tax table such that each individual pays the same amount of tax as before elimination of surtax? Note that number of tax brackets and the tax rate in each bracket would be modified. Assume there is no tax credit.