Subjects algebra

Exchange Rate Cost 94E855

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1. **Problem statement:** Estimate the amount Ann will receive when exchanging money using the given graphs. 2. **Exchange rate graph (pounds vs Singapore dollars):** The graph is linear, so we can find the exchange rate by using two points. From the description, the graph goes from (0 dollars, 0 pounds) to (240 dollars, 120 pounds). 3. **Calculate the exchange rate:** $$\text{Exchange rate} = \frac{120 \text{ pounds}}{240 \text{ dollars}} = \frac{1}{2} \text{ pounds per dollar}$$ 4. **(i) Pounds received for dollars:** (a) For $170 dollars: $$170 \times \frac{1}{2} = 85 \text{ pounds}$$ (b) For $50 dollars: $$50 \times \frac{1}{2} = 25 \text{ pounds}$$ 5. **(ii) Dollars received for pounds:** Since $1 dollar = \frac{1}{2}$ pounds, then $1$ pound = $2$ dollars. (a) For £60: $$60 \times 2 = 120 \text{ dollars}$$ (b) For £24: $$24 \times 2 = 48 \text{ dollars}$$ --- 6. **Cost graph (cost $C$ vs mass $m$):** The graph is linear from (0 kg, $0) to (100 kg, $300). 7. **Calculate cost per kg:** $$\text{Cost per kg} = \frac{300}{100} = 3 \text{ dollars per kg}$$ 8. **(i) Cost for given mass:** (a) For 40 kg: $$40 \times 3 = 120 \text{ dollars}$$ (b) For 76 kg: $$76 \times 3 = 228 \text{ dollars}$$ 9. **(ii) Mass for given cost:** (a) For $50: $$m = \frac{50}{3} \approx 16.67 \text{ kg}$$ (b) For $260: $$m = \frac{260}{3} \approx 86.67 \text{ kg}$$