1. Let's define variables for the prices: - Let $C$ be the cost of one coat. - Let $S$ be the cost of one pair of shoes. - Let $J$ be the cost of one pair of jeans. - Let $K$ be the cost of one pair of socks. 2. From the problem, we have the following relationships: - Six pairs of shoes cost as much as 1 coat: $$6S = C$$ - Two pairs of jeans cost as much as 3 pairs of shoes: $$2J = 3S$$ - Four pairs of socks cost as much as one pair of jeans: $$4K = J$$ 3. We want to find how many coats can be exchanged for 64 pairs of socks. First, express the cost of 64 pairs of socks in terms of $C$. 4. From $$4K = J$$, we get $$K = \frac{J}{4}$$. 5. From $$2J = 3S$$, we get $$J = \frac{3S}{2}$$. 6. Substitute $J$ into $K$: $$K = \frac{3S}{2 \times 4} = \frac{3S}{8}$$ 7. The cost of 64 pairs of socks is: $$64K = 64 \times \frac{3S}{8} = 8 \times 3S = 24S$$ 8. From $$6S = C$$, we get $$S = \frac{C}{6}$$. 9. Substitute $S$ into the cost of 64 socks: $$24S = 24 \times \frac{C}{6} = 4C$$ 10. Therefore, 64 pairs of socks cost as much as 4 coats. **Final answer:** You can exchange 64 pairs of socks for 4 coats.