1. **State the problem:** We need to calculate the income tax Artem pays on his gross earnings with a tiered tax rate and an annual tax credit. 2. **Tax rules:** - 20% tax on the first 44,000 - 40% tax on any amount above 44,000 - Subtract annual tax credit from total tax 3. **Part (a) Calculation:** - Artem's gross earnings: 55,000 - Taxable amount above 44,000: $$55,000 - 44,000 = 11,000$$ - Tax on first 44,000: $$44,000 \times 0.20 = 8,800$$ - Tax on balance 11,000: $$11,000 \times 0.40 = 4,400$$ - Total tax before credit: $$8,800 + 4,400 = 13,200$$ - Subtract tax credit: $$13,200 - 4,000 = 9,200$$ 4. **Answer for (a):** Artem pays $$9,200$$ in income tax for the year. 5. **Part (b) Problem:** Artem paid 14,000 in tax including a bonus payment. We need to find the bonus amount. 6. **Set up equation:** Let bonus be $$b$$. Total gross earnings including bonus: $$55,000 + b$$ Tax on first 44,000: $$8,800$$ (fixed) Tax on balance: $$0.40 \times ((55,000 + b) - 44,000) = 0.40 \times (11,000 + b) = 4,400 + 0.40b$$ Total tax before credit: $$8,800 + 4,400 + 0.40b = 13,200 + 0.40b$$ After subtracting tax credit 4,000, tax paid is: $$13,200 + 0.40b - 4,000 = 9,200 + 0.40b$$ 7. **Use given tax paid:** $$9,200 + 0.40b = 14,000$$ 8. **Solve for bonus:** $$0.40b = 14,000 - 9,200 = 4,800$$ $$b = \frac{4,800}{0.40}$$ Show cancellation: $$b = \frac{\cancel{4,800}}{\cancel{0.40}} = 12,000$$ 9. **Answer for (b):** The bonus Artem received is $$12,000$$.