Final answer:
The expression to show the total number of letters Yuan wrote is 15m, where m represents the number of months.
Step-by-step explanation:
To find out how many total letters Yuan wrote, you can use an algebraic expression to represent the situation. If Yuan wrote 15 letters each month, and this continued for a certain number of months, you can use the variable m to represent the number of months. The expression would be 15m. So if Yuan did this for 5 months, for example, you would calculate the total number of letters as 15 x 5 = 75 letters.