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

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
; 5b+10c=12,500

Answer 1

To model the situation with a pair of linear equations, we need to consider the two given constraints:

1. The total number of items (bags and caps) is 2,000.
2. The total cost of the items cannot exceed $12,500.

Let \( b \) represent the number of bags and \( c \) represent the number of caps.

The equations derived from the constraints will be:

1. The total number of items equation:
\[
b + c = 2000
\]

2. The total cost equation:
Since each bag costs $10 and each cap costs $5, the total cost can be modeled as:
\[
10b + 5c = 12500
\]

Thus, the correct pair of linear equations that model this situation is:
\[
b + c = 2000
\]
\[
10b + 5c = 12500
\]

So the correct response would be:
- \( b + c = 2000 \)
- \( 10b + 5c = 12500 \)