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
Let's denote the number of bags as b and the number of caps as c.
From the given information, we can write the following equations:
Equation 1: The total number of items is equal to 2,000:
b + c = 2,000
Equation 2: The total cost of bags and caps should not exceed the budget of $12,500:
10b + 5c ≤ 12,500
So, the pair of linear equations that model this situation are:
Equation 1: b + c = 2,000
Equation 2: 10b + 5c ≤ 12,500
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)
To create a pair of linear equations that model this situation, let's assume the number of bags given away is represented by the variable 'x', and the number of caps given away is represented by the variable 'y'.
According to the given information:
1. The cost of each bag is $10, so the total cost of bags will be 10x dollars.
2. The cost of each cap is $5, so the total cost of caps will be 5y dollars.
3. The total number of items given away (bags + caps) is 2,000, so x + y = 2,000.
4. The total budget allocated for the items given away is $12,500, so 10x + 5y = 12,500.
Hence, the pair of linear equations that model this situation are:
x + y = 2,000
10x + 5y = 12,500.