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=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 ; 10 b plus 10 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=12,500; 5b+10c=2,000
b+c=2,000; 10b+5c=12,500
b+c=2,000; 10b+5c=12,500
The correct pair of linear equations that model this situation is:
b + c = 2,000 (equation 1)
10b + 5c = 12,500 (equation 2)
Explanation:
Let's break down the problem and identify the variables and constraints given.
The problem states that the Jackson Jammers are giving away bags (b) and caps (c) at their next game. They plan to give away a total of 2,000 items, and they have a budget of $12,500. From this information, we can form two equations.
1. The first equation represents the total number of items given away, which is the sum of the bags and caps: b + c = 2,000.
2. The second equation represents the budget constraint. The cost of each bag is $10, so the total cost of bags is 10b. The cost of each cap is $5, so the total cost of caps is 5c. Therefore, the total cost of the items given away is 10b + 5c. Since their budget is $12,500, we can set up the equation: 10b + 5c = 12,500.
Thus, the correct pair of linear equations is b + c = 2,000 and 10b + 5c = 12,500.