A ski lodge offers two weekend packages. Package A provides 2 nights and 3 meals for $280. Package B provides 2 nights and 5 meals for $320.

A ski lodge offers two weekend packages. Package A provides 2 nights and 3 meals for $280. Package B provides 2 nights and 5 meals for $320. Write and solve a system of equations to find the costs per night and per meal. (Assume the cost per night and cost per meal are the same for both packages.) Use n to represent the cost per night and m to represent the cost of each meal. (8 points)
Step 1: The equation representing package A is given. Complete the system of equations by writing an equation to represent package B. (1 point)
Package A: 2n + 3m = 280
Package B: _2n + 5m = 320__________________

Step 2: Select a method for solving the system. Which method did you choose? Why? (2 points)

Step 3: Solve the system of equations to find the costs per night and per meal. Show your work.(3 points)