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 a pair of linear equations that model this situation.
A. b + c = 12,500; 5b + 10c = 2,000
B. b + c = 12,500; 10b + 5c = 2,000
C. b + c = 2,000; 10b + 5c = 12,500
D. b + c = 2,000; 5c + 10b = 12,500
PLS HELP.
The correct pair of linear equations that models this situation is:
D. b + c = 2,000; 5c + 10b = 12,500
This is because the first equation represents the total number of items being given away, where b represents the number of bags and c represents the number of caps. The second equation represents the cost of the items, where 10b represents the cost of the bags and 5c represents the cost of the caps.
The correct pair of linear equations that model this situation is:
B. b + c = 12,500; 10b + 5c = 2,000
Let's break down the explanation:
In the first equation, b + c = 12,500, we are representing the total number of items given away, which is 2,000, as the sum of the bags (b) and the caps (c). This equation accounts for the total quantity of items.
In the second equation, 10b + 5c = 2,000, we are representing the total cost spent on bags and caps, given a budget of $12,500. The bags cost $10 each, so the cost of bags (10b) is multiplied by the number of bags (b). The caps cost $5 each, so the cost of caps (5c) is multiplied by the number of caps (c). This equation accounts for the budget constraints.
Therefore, option B. b + c = 12,500; 10b + 5c = 2,000, correctly models the given situation.
To write a pair of linear equations that model this situation, we need to represent the number of bags and caps given away as well as the cost constraints.
Let's assign variables b to represent the number of bags and c to represent the number of caps.
The first equation to represent the total number of items given away is b + c = 2,000. This equation states that the sum of the number of bags and the number of caps given away is equal to 2,000 items.
The second equation to represent the cost constraint is 10b + 5c = 12,500. This equation states that the cost of the bags, which is $10 per bag multiplied by the number of bags, plus the cost of the caps, which is $5 per cap multiplied by the number of caps, is equal to their budget of $12,500.
So, the correct answer is A. b + c = 12,500; 5b + 10c = 2,000.