1. **State the problem:** We are given two ratios involving jellies, mints, and toffees: - Jellies to mints: $7n : 3$ - Mints to toffees: $5 : 8n$ We need to find the ratio of jellies to toffees in simplest form. 2. **Write down the ratios clearly:** $$\frac{\text{jellies}}{\text{mints}} = \frac{7n}{3}$$ $$\frac{\text{mints}}{\text{toffees}} = \frac{5}{8n}$$ 3. **Find a common term to link the ratios:** Since both ratios involve mints, we can express jellies and toffees in terms of mints and then find the ratio jellies to toffees. 4. **Express jellies in terms of mints:** $$\text{jellies} = \frac{7n}{3} \times \text{mints}$$ 5. **Express toffees in terms of mints:** From the second ratio: $$\frac{\text{mints}}{\text{toffees}} = \frac{5}{8n} \implies \text{toffees} = \frac{8n}{5} \times \text{mints}$$ 6. **Form the ratio jellies to toffees:** $$\frac{\text{jellies}}{\text{toffees}} = \frac{\frac{7n}{3} \times \text{mints}}{\frac{8n}{5} \times \text{mints}} = \frac{7n}{3} \times \frac{5}{8n}$$ 7. **Simplify the expression:** $$= \frac{7n \times 5}{3 \times 8n} = \frac{35n}{24n}$$ 8. **Cancel common factors:** $$= \frac{\cancel{35} \cancel{n}}{\cancel{24} \cancel{n}} = \frac{35}{24}$$ Since 35 and 24 have no common factors other than 1, the ratio is already in simplest form. **Final answer:** $$\boxed{35 : 24}$$