Question

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) Responses b+c=12,500 ; 5b+10c=2,000 b plus c equals 12,500 ; 5 b plus 10 c equals 2,000 b+c=12,500 ; 10b+5c=2,000 b plus c equals 12,500 ; 10 b plus 5 c equals 2,000 b+c=2,000 ; 10b+5c=12,500 b plus c equals 2,000 ; 10 b plus 5 c equals 12,500 b+c=2,000 ; 5b+10c=12,500

Answer 1

To model the situation with a pair of linear equations, let's define the variables:
- Let \( b \) represent the number of bags.
- Let \( c \) represent the number of caps.

From the problem statement, we have the following information:

1. The total number of items (bags and caps) is 2,000:
\[
b + c = 2000
\]

2. The total cost for the bags and caps must not exceed the budget of $12,500. Given that each bag costs $10 and each cap costs $5, the cost equation can be set up as:
\[
10b + 5c = 12500
\]

So, the pair of linear equations that model this situation is:
1. \( b + c = 2000 \)
2. \( 10b + 5c = 12500 \)

Thus, the correct response from the options provided would be:
\( b + c = 2000 ; 10b + 5c = 12500 \)