1. **State the problem:** Pete and Maeve are saving money to buy an Xbox costing 200. 2. **Pete's savings:** - Initial amount: 20 - Weekly saving: 12 (i) Total after 5 weeks: $$\text{Total} = 20 + 12 \times 5$$ $$= 20 + 60 = 80$$ (ii) Expression for total after $n$ weeks: $$\text{Pete's savings} = 20 + 12n$$ 3. **Maeve's savings:** - Initial amount: 15 - Weekly saving: 6 Expression for total after $n$ weeks: $$\text{Maeve's savings} = 15 + 6n$$ 4. **Money given to buy Xbox:** - Pete gives one quarter: $$\frac{1}{4}(20 + 12n)$$ - Maeve gives two thirds: $$\frac{2}{3}(15 + 6n)$$ 5. **Total money given to buy Xbox:** $$\frac{1}{4}(20 + 12n) + \frac{2}{3}(15 + 6n) \geq 200$$ 6. **Solve inequality:** Multiply both sides by 12 (LCM of 4 and 3) to clear denominators: $$12 \times \left(\frac{1}{4}(20 + 12n) + \frac{2}{3}(15 + 6n)\right) \geq 12 \times 200$$ $$3(20 + 12n) + 8(15 + 6n) \geq 2400$$ $$60 + 36n + 120 + 48n \geq 2400$$ $$180 + 84n \geq 2400$$ Subtract 180 from both sides: $$\cancel{180} + 84n \geq 2400 - \cancel{180}$$ $$84n \geq 2220$$ Divide both sides by 84: $$\frac{\cancel{84}n}{\cancel{84}} \geq \frac{2220}{84}$$ $$n \geq \frac{2220}{84}$$ Simplify fraction: $$n \geq \frac{2220 \div 12}{84 \div 12} = \frac{185}{7} \approx 26.43$$ 7. **Interpretation:** They will have enough money after 27 weeks (since $n$ must be whole weeks). **Final answers:** (i) Pete's total after 5 weeks: 80 (ii) Pete's savings after $n$ weeks: $$20 + 12n$$ (b) Maeve's savings after $n$ weeks: $$15 + 6n$$ (c) They will have enough money after 27 weeks.