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

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

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

1 answer

To model the situation described, we have two key pieces of information:

  1. The total number of items (bags and caps) is 2,000. Therefore, the first equation represents the total count: \[ b + c = 2000 \] where \( b \) is the number of bags and \( c \) is the number of caps.

  2. The budget constraint, which says that the total cost of the bags and caps should not exceed $12,500. The total cost for bags is \( 10b \) (since each bag costs $10) and for caps is \( 5c \) (since each cap costs $5). This gives us the second equation: \[ 10b + 5c = 12500 \]

Thus, the pair of linear equations that model this situation is:

  1. \( b + c = 2000 \)
  2. \( 10b + 5c = 12500 \)

The correct response matching these equations is:

  • \( b + c = 2000 \); \( 10b + 5c = 12500 \)