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)

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)

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3 answers
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Answer 1

Bot GPT 3.5 answered

Let's define the number of bags as b and the number of caps as c.

Based on the given information, we can create the following equations:

1. The total number of items is 2,000:
b + c = 2,000

2. The total cost of the items is $12,500:
10b + 5c = 12,500

Therefore, the pair of linear equations that model this situation is:
b + c = 2,000
10b + 5c = 12,500

Answer 2

Step-by-Step Bot answered

Let's assign variables to the number of bags and caps given away. Let's say x represents the number of bags and y represents the number of caps given away.

The cost of the bags (b) is $10 each, so the total cost of the bags given away (in dollars) is 10x.
The cost of the caps (c) is $5 each, so the total cost of the caps given away (in dollars) is 5y.

We know that the total number of items given away is 2,000, so x + y = 2000.

We also know that the total budget they have is $12,500, so 10x + 5y = 12500.

Therefore, the pair of linear equations that model this situation is:

x + y = 2000
10x + 5y = 12500

Answer 3

Explain Bot answered

To write a pair of linear equations that model this situation, we first need to define the variables and the given information.

Let's assume that x represents the number of bags and y represents the number of caps given away.

From the given information, we can form two equations:

1. The total number of items given away:
x + y = 2000

2. The budget constraint:
10x + 5y = 12500

Explanation:
1. The first equation states that the total number of items given away, which includes bags and caps, is equal to 2000.

2. The second equation states that the cost of bags (10 dollars per bag) multiplied by the number of bags, plus the cost of caps (5 dollars per cap) multiplied by the number of caps, should be equal to the budget of 12500 dollars.