1. **Problem (a):** Jacob buys a kayak priced at 870. It is reduced by 15%, then a further 10% reduction is applied. 2. **Formula:** To find the final price after successive percentage reductions, multiply the original price by the complements of the percentages in decimal form: $$\text{Final Price} = \text{Original Price} \times (1 - r_1) \times (1 - r_2)$$ where $r_1$ and $r_2$ are the reduction rates. 3. **Calculate first reduction:** $$870 \times (1 - 0.15) = 870 \times 0.85 = 739.5$$ 4. **Calculate second reduction:** $$739.5 \times (1 - 0.10) = 739.5 \times 0.90 = 665.55$$ 5. **Answer (a):** Jacob pays **665.55** for the kayak. 1. **Problem (b):** Paddle costs 95 dollars. Jacob thinks exchange rate is 1 euro = 1.183 dollars. Actual rate is 1 euro = $d$ dollars. The paddle costs 1.02 euros more than Jacob thought. 2. **Formula:** Cost in euros = Cost in dollars divided by exchange rate. 3. **Jacob's expected cost in euros:** $$\frac{95}{1.183} \approx 80.29$$ 4. **Actual cost in euros:** $$80.29 + 1.02 = 81.31$$ 5. **Set up equation for actual rate $d$:** $$\frac{95}{d} = 81.31$$ 6. **Solve for $d$:** $$d = \frac{95}{81.31} \approx 1.168$$ 7. **Answer (b):** The actual exchange rate $d$ is approximately **1.168**. 1. **Problem (c):** Jacob kayaks from S to A (2 km) at 6 km/h, then runs from A to F (8 km) at 12 km/h. 2. **Formula:** Time = Distance / Speed. 3. **Kayaking time:** $$\frac{2}{6} = \frac{1}{3} \text{ hours} = 20 \text{ minutes}$$ 4. **Running time:** $$\frac{8}{12} = \frac{2}{3} \text{ hours} = 40 \text{ minutes}$$ 5. **Total time:** $$\frac{1}{3} + \frac{2}{3} = 1 \text{ hour} = 60 \text{ minutes}$$ 6. **Answer (c):** Total time is **1 hour**. 1. **Problem (d):** Find time to kayak directly from S to F. 2. **Use Pythagoras theorem:** $$|SF| = \sqrt{(SA)^2 + (AF)^2} = \sqrt{2^2 + 8^2} = \sqrt{4 + 64} = \sqrt{68}$$ 3. **Calculate $|SF|$:** $$\sqrt{68} \approx 8.246$$ 4. **Time to kayak directly:** $$\frac{8.246}{6} \approx 1.374 \text{ hours}$$ 5. **Convert to minutes:** $$1.374 \times 60 \approx 82.44 \text{ minutes}$$ 6. **Answer (d):** Time is approximately **82 minutes**.