1. **Stating the problem:** Bill changes 450 pounds and gets 711 dollars. Gwyll changes 500 pounds and gets 820 dollars. We need to find the exchange rates for both and determine who got the better deal. 2. **Formula used:** Exchange rate is calculated by dividing the amount of dollars received by the amount of pounds exchanged. $$\text{Exchange rate} = \frac{\text{Dollars received}}{\text{Pounds exchanged}}$$ 3. **Calculating Bill's exchange rate:** $$\text{Bill's rate} = \frac{711}{450} = 1.58$$ This means Bill got 1.58 dollars for every 1 pound. 4. **Calculating Gwyll's exchange rate:** $$\text{Gwyll's rate} = \frac{820}{500} = 1.64$$ This means Gwyll got 1.64 dollars for every 1 pound. 5. **Comparing the exchange rates:** Since 1.64 > 1.58, Gwyll got a better deal because he received more dollars per pound. **Final answers:** - a) Bill's exchange rate: $1.58$ - b) Gwyll's exchange rate: $1.64$ - c) Gwyll got the better deal.