Let's define the number of bags as b and the number of caps as c.
Based on the given information, we can create the following equations:
1. The total number of items is 2,000:
b + c = 2,000
2. The total cost of the items is $12,500:
10b + 5c = 12,500
Therefore, the pair of linear equations that model this situation is:
b + c = 2,000
10b + 5c = 12,500