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.

Answer 1

To model the situation with a pair of linear equations, we can set up the variables and establish the equations based on the information provided.

Let:

• \( b \) = number of bags
• \( c \) = number of caps

From the information given, we can extract the following two equations:

1. Total items equation: Since they plan to give away a total of 2,000 items (bags and caps), we can write the equation: \[ b + c = 2000 \]

2. Budget equation: The cost of the bags is $10 each and the cost of the caps is $5 each, with a total budget of $12,500. This can be expressed as: \[ 10b + 5c = 12500 \]

Thus, the pair of linear equations that model this situation is: \[ \begin{align*} b + c & = 2000 \quad \text{(1)} \ 10b + 5c & = 12500 \quad \text{(2)} \end{align*} \]