To model this situation, we need two equations based on the information provided:
- The total number of items (bags and caps) is 2,000.
- The total cost of the items is $12,500.
Let:
- \( b \) be the number of bags.
- \( c \) be the number of caps.
From the first piece of information, we have: \[ b + c = 2000 \] (Equation 1)
From the second piece of information, we express the total cost: The cost of bags is $10 each, and the cost of caps is $5 each. Therefore: \[ 10b + 5c = 12500 \] (Equation 2)
So, the pair of linear equations that model the situation is: \[ b + c = 2000 \] \[ 10b + 5c = 12500 \]
The correct answer is: b+c=2,000; 10b+5c=12,500