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)
Responses
b+c=2,000; 5b+10c=12,500
b plus c equals 2,000 ; 10 b plus 10 c equals 12,500
b+c=12,500; 5b+10c=2,000
b plus c equals 12,500 ; 5 b plus 10 c equals 2,000
b+c=2,000; 10b+5c=12,500
b plus c equals 2,000 ; 10 b plus 5 c equals 12,500
b+c=12,500; 10b+5c=2,000
b plus c equals 12,500 ; 10 b plus 5 c equals 2,000
b plus c equals 2,000 ; 10 b plus 5 c equals 12,500
The correct pair of linear equations that model this situation is:
b + c = 2,000
5b + 10c = 12,500
Explanation:
To find the correct pair of linear equations, we need to consider the two given conditions:
1. The total number of items given away is 2,000.
2. The budget for the giveaway is $12,500.
First, let's consider the total number of items given away. Since we are giving away bags (b) and caps (c), the sum of bags and caps must be equal to 2,000. Therefore, our first equation is:
b + c = 2,000
Next, let's consider the budget. Each bag costs $10 and each cap costs $5. So, the total cost of bags and caps can be calculated by multiplying the number of bags (b) by $10 and the number of caps (c) by $5. This value must be equal to the budget of $12,500. Therefore, our second equation is:
5b + 10c = 12,500
Hence, the correct pair of linear equations that model this situation is:
b + c = 2,000
5b + 10c = 12,500