1. **Problem statement:** Alain and Beatrice share 750 in the ratio 8:7. Show Alain receives 400. 2. **Step 1: Understand ratio division** The total parts in the ratio are $8 + 7 = 15$ parts. 3. **Step 2: Calculate value of one part** $$\text{One part} = \frac{750}{15} = 50$$ 4. **Step 3: Calculate Alain's share** Alain's share = $8 \times 50 = 400$ Thus, Alain receives 400. --- 5. **(ii)(a) Write 150 as a percentage of 400** 6. **Step 1: Use percentage formula** $$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 = \frac{150}{400} \times 100$$ 7. **Step 2: Simplify fraction** $$\frac{150}{400} = \frac{\cancel{150}}{\cancel{400}} = \frac{15}{40}$$ 8. **Step 3: Calculate percentage** $$\frac{15}{40} \times 100 = 37.5\%$$ --- 9. **(ii)(b) Calculate amount after 5 years simple interest on 250 at 2% per year** 10. **Step 1: Use simple interest formula** $$I = P \times r \times t$$ where $P=250$, $r=0.02$, $t=5$ 11. **Step 2: Calculate interest** $$I = 250 \times 0.02 \times 5 = 25$$ 12. **Step 3: Calculate total amount** $$A = P + I = 250 + 25 = 275$$ --- 13. **(iii) Calculate amount Beatrice has after 5 years compound interest at 0.25% per month** 14. **Step 1: Identify parameters** Principal $P=350$, monthly rate $r=0.0025$, time $t=5$ years, compounding monthly means $n=12$ times per year. 15. **Step 2: Calculate total number of compounding periods** $$nt = 12 \times 5 = 60$$ 16. **Step 3: Use compound interest formula** $$A = P \left(1 + r\right)^{nt} = 350 \left(1 + 0.0025\right)^{60}$$ 17. **Step 4: Calculate inside the parentheses** $$1 + 0.0025 = 1.0025$$ 18. **Step 5: Calculate power** $$1.0025^{60} \approx 1.1616$$ 19. **Step 6: Calculate amount** $$A = 350 \times 1.1616 = 406.56$$ 20. **Step 7: Round to nearest dollar** $$407$$ --- **Final answers:** - Alain receives 400. - 150 is 37.5% of 400. - Amount Alain has after 5 years is 275. - Amount Beatrice has after 5 years is 407.