1. The problem is to calculate the tax payable based on income brackets and tax rates. 2. The tax brackets and rates are: - $0-$15000: 0% tax - $15001-$40000: 15% tax on amount over $15000 - $40001-$90000: 25% tax on amount over $40000 plus tax from previous bracket - $90001 and above: 33% tax on amount over $90000 plus tax from previous brackets 3. The formula for tax payable in each bracket is: - For income $I$ in $0 \leq I \leq 15000$, tax = $0$ - For $15001 \leq I \leq 40000$, tax = $0 + 0.15 \times (I - 15000)$ - For $40001 \leq I \leq 90000$, tax = tax on $40000 + 0.25 \times (I - 40000)$ - For $I > 90000$, tax = tax on $90000 + 0.33 \times (I - 90000)$ 4. Calculate tax on $40000$: $$\text{tax on }40000 = 0 + 0.15 \times (40000 - 15000) = 0.15 \times 25000 = 3750$$ 5. Calculate tax on $90000$: $$\text{tax on }90000 = 3750 + 0.25 \times (90000 - 40000) = 3750 + 0.25 \times 50000 = 3750 + 12500 = 16250$$ 6. Therefore, the tax payable for any income $I$ is: - If $I \leq 15000$, tax = $0$ - If $15000 < I \leq 40000$, tax = $0.15 \times (I - 15000)$ - If $40000 < I \leq 90000$, tax = $3750 + 0.25 \times (I - 40000)$ - If $I > 90000$, tax = $16250 + 0.33 \times (I - 90000)$ This stepwise calculation ensures correct tax payable based on income brackets.