Question

The Jackson jammers are giving away bags and caps at their next game. The ags, 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 described, we need to set up a pair of linear equations based on the information given.

Let:
- \( b \) = number of bags
- \( c \) = number of caps

From the problem, we know two key pieces of information:

1. The total number of items (bags and caps) they plan to give away is 2,000. This gives us our first equation:
\[
b + c = 2000
\]

2. The total cost of the bags and caps must not exceed their budget of $12,500. The cost of each bag is $10 and the cost of each cap is $5. This gives us our second equation:
\[
10b + 5c = 12500
\]

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