1. **Stating the problem:** A notebook costs floui times the price of a pencil. The pencil costs 30p less than the notebook. We need to find the price of the notebook. 2. **Define variables:** Let the price of the pencil be $x$ pence. 3. **Express the notebook price:** The notebook costs floui times the pencil, so notebook price = $floui \times x$. 4. **Use the given relation:** The pencil costs 30p less than the notebook, so: $$x = floui \times x - 30$$ 5. **Solve for $x$:** $$x - floui \times x = -30$$ $$x(1 - floui) = -30$$ $$x = \frac{-30}{1 - floui} = \frac{30}{floui - 1}$$ 6. **Find notebook price:** $$\text{notebook} = floui \times x = floui \times \frac{30}{floui - 1} = \frac{30 \times floui}{floui - 1}$$ 7. **Check options:** The notebook price must be one of 40p, 60p, 50p, or 70p. We can test each to find a consistent $floui$. - For notebook = 60p: $$60 = \frac{30 \times floui}{floui - 1}$$ Multiply both sides by $(floui - 1)$: $$60(floui - 1) = 30 floui$$ $$60 floui - 60 = 30 floui$$ $$60 floui - 30 floui = 60$$ $$30 floui = 60$$ $$floui = 2$$ 8. **Check pencil price:** $$x = \frac{30}{floui - 1} = \frac{30}{2 - 1} = 30p$$ 9. **Verify pencil cost:** Pencil is 30p less than notebook: $$60p - 30p = 30p$$ which matches $x$. **Answer:** The price of the notebook is 60p.