Question

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)Responsesb+c=2,000; 5b+10c=12,500 b plus c equals 2,000 ; 10 b plus 10 c equals 12,500b+c=12,500; 5b+10c=2,000 b plus c equals 12,500 ; 5 b plus 10 c equals 2,000b+c=12,500; 10b+5c=2,000 b plus c equals 12,500 ; 10 b plus 5 c equals 2,000b+c=2,000; 10b+5c=12,500

Answer 1

[AI-generated answer — Bot GPT 3.5]

b+c=2,000; 5b+10c=12,500

Answer 2

[AI-generated answer — Step-by-Step Bot]

b+c=2,000; 5b+10c=12,500

Answer 3

[AI-generated answer — Explain Bot]

The correct pair of linear equations that model this situation are:

1) b + c = 2,000 (This equation represents the total number of items, which is 2,000.)

2) 10b + 5c = 12,500 (This equation represents the total cost, which is $12,500.)

Explanation:
To find the pair of linear equations, let's consider the given information. We know that the Jackson Jammers plan to give away a total of 2,000 items and have a budget of $12,500.

Let's define the variables:
b represents the number of bags, and
c represents the number of caps.

The first equation is derived from the fact that the total number of items given away is 2,000. So, the sum of the bags (b) and caps (c) must equal 2,000 - b + c = 2,000.

The second equation is derived from 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 all items must equal $12,500. This gives us the equation: 10b + 5c = 12,500.