Problem 5.7. In a magic shop, for 20 silver coins you can buy an invisibility cloak and get 4 gold coins as change. For 15 silver coins you can buy an invisibility cloak and get 1 gold coin as change. How many silver coins will you get as change if you buy an invisibility cloak for 14 gold coins?
Answer: 10.

Solution. In the first case, compared to the second, by paying 5 extra silver coins, one can receive 3 extra gold coins in change. Therefore, 5 silver coins are equivalent to 3 gold coins.

In the second case, by paying 15 silver coins (which is equivalent to $3 \cdot 3=9$ gold coins), one can get the cloak and 1 gold coin in change. Therefore, the cloak costs 8 gold coins.

In the third case, by paying 14 gold coins for a cloak worth 8 coins, one would receive 6 gold coins in change, which is equivalent to $5 \cdot 2=10$ silver coins.