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)
We can create two equations to represent the given situation.
Let's define the variables:
b = number of bags
c = number of caps
The first equation represents the total number of items:
b + c = 2000
The second equation represents the budget:
10b + 5c = 12500
Let's represent the number of bags as 'x' and the number of caps as 'y'.
The cost of each bag, 'b', is $10, and the cost of each cap, 'c', is $5.
So, the total cost of bags will be 10x, and the total cost of caps will be 5y.
The total number of items given away is 2,000. So, the equation representing this is:
x + y = 2,000
The total budget for the giveaway is $12,500. So, the equation representing this is:
10x + 5y = 12,500
Therefore, the pair of linear equations that model this situation is:
x + y = 2,000
10x + 5y = 12,500
To model this situation with linear equations, we can use the following information:
1. The bags cost $10 each, denoted by b.
2. The caps cost $5 each, denoted by c.
3. The total number of items to be given away is 2,000.
Let's break down the problem step by step:
1. Define the variables:
Let's use the variable x to represent the number of bags, and y to represent the number of caps.
2. Write the equations:
Since "The bags cost $10 each," the cost of the bags in terms of the number of bags (x) is 10x.
Similarly, since "The caps cost $5 each," the cost of the caps in terms of the number of caps (y) is 5y.
Therefore, the first equation represents the cost of the bags:
10x + 5y = 12,500
Since "The total number of items to be given away is 2,000," the sum of the bags and caps should be equal to 2,000:
x + y = 2,000
So, the pair of linear equations that model this situation are:
10x + 5y = 12,500
x + y = 2,000