the Jackson jammers are giving away bags and caps at their next game. the bags,b, cost them 10$ each. the caps,c, cost them 5$ each, they plan to give away 2,000 tota; items and have a budget of $12,500. write the pair of linear equations that model this situation

Answer 1

Let's say the number of bags they give away is represented by x, and the number of caps they give away is represented by y.

1) The cost of the bags: The cost of each bag is $10, and they give away x bags, so the total cost of the bags is 10x dollars: 10x = cost of the bags.

2) The cost of the caps: The cost of each cap is $5, and they give away y caps, so the total cost of the caps is 5y dollars: 5y = cost of the caps.

3) The total number of items given away: They plan to give away 2,000 items in total, so the sum of the bags and caps given away must equal 2,000: x + y = 2,000.

4) The budget: They have a budget of $12,500. The total cost of the bags (10x) plus the total cost of the caps (5y) must be less than or equal to $12,500: 10x + 5y ≤ 12,500.

Therefore, the pair of linear equations that model this situation is:
10x = cost of the bags (equation 1)
5y = cost of the caps (equation 2)
x + y = 2,000 (equation 3)
10x + 5y ≤ 12,500 (equation 4)