1. **State the problem:** Olivia, Leon, and Ruby sold a total of 56 games. The ratio of the numbers of games they sold is 4 : 3 : 1. We need to find how many more games Leon sold than Ruby. 2. **Understand the ratio:** The ratio 4 : 3 : 1 means for every 4 games Olivia sold, Leon sold 3, and Ruby sold 1. 3. **Calculate the total parts:** Add the parts of the ratio: $$4 + 3 + 1 = 8$$ parts in total. 4. **Find the value of one part:** Since the total games sold is 56, each part represents $$\frac{56}{8} = 7$$ games. 5. **Calculate the number of games each person sold:** - Olivia sold $$4 \times 7 = 28$$ games. - Leon sold $$3 \times 7 = 21$$ games. - Ruby sold $$1 \times 7 = 7$$ games. 6. **Find how many more games Leon sold than Ruby:** $$21 - 7 = 14$$ games. **Final answer:** Leon sold 14 more games than Ruby.