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
b plus c equals 2,000 ; 5 b plus 10 c equals 12,500
b plus c equals 12,500 ; 5 b plus 10 c equals 2,000
To write the pair of linear equations that model this situation, we need to consider the cost of the bags and the caps, as well as the total number of items and the budget.
Let's define:
b = the number of bags
c = the number of caps
1. The first equation represents the total number of items:
b + c = 2,000
This equation states that the sum of the number of bags and the number of caps equals 2,000, which is the total number of items being given away.
2. The second equation represents the budget:
$10b + $5c = $12,500
This equation states that the cost of the bags (10 dollars per bag) multiplied by the number of bags, plus the cost of the caps (5 dollars per cap) multiplied by the number of caps, equals the total budget of $12,500.
Therefore, the correct pair of linear equations that model this situation is:
b + c = 2,000
$10b + $5c = $12,500
or
b+c=2,000; 10b+5c=12,500