The Jackson Jammers are giving away bags and caps at their next game. The bags, b , cost them $10 each, and the caps, c , cost them $5 each. They plan to give away 2,000 total items and have a budget of $12,500. Write the pair of linear equations that model this situation.(1 point)

Question

b+c=12,500; 10b+5c=2,000

b+c=12,500; 5b+10c=2,000

b+c=2,000; 5b+10c=12,500

b+c=2,000; 10b+5c=12,500

Answer 1

To model this situation, we need two equations based on the information provided:

1. The total number of items (bags and caps) is 2,000.
2. 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