Real-World Systems of Equations Quick Check

Question

2 of 52 of 5 Items
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)
Responses

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

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

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; 5b+10c=2,000

Answer 1

To model the situation described, we need to write a pair of linear equations based on the quantities of bags and caps, their costs, and the total items and budget constraints.

1. Let \( b \) be the number of bags and \( c \) be the number of caps.

2. They plan to give away a total of 2,000 items: \[ b + c = 2,000 \]

3. The total cost for the bags and caps cannot exceed $12,500. Given that each bag costs $10 and each cap costs $5, the equation for the budget constraint is: \[ 10b + 5c = 12,500 \]

Thus, the pair of linear equations that model the situation is: \[ b + c = 2,000 \] \[ 10b + 5c = 12,500 \]

This corresponds to the option: b + c = 2,000; 10b + 5c = 12,500.