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

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

Answer 1

To model the situation with a pair of linear equations, we need to establish two equations based on the given information about the items and the budget.

1. Total Items: The Jackson Jammers plan to give away a total of 2,000 items, which consists of bags (b) and caps (c). Therefore, the first equation is: \[ b + c = 2000 \]

2. Budget: Each bag costs $10 and each cap costs $5. They have a total budget of $12,500. The second equation can be represented as: \[ 10b + 5c = 12500 \]

Now, we can look at the response options you provided. The correct set of equations that match our analysis is:

• b + c = 2000
• 10b + 5c = 12500

So, the right response is: b + c = 2000; 10b + 5c = 12500 (this response is not explicitly listed among the choices you offered, but these are the correct equations). Make sure to apply this into your context for accuracy.