Question

2. 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: ___________________ 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) Step 4: Explain the meaning of the solutions for m and n. (2 points: 1 point each)

Answer 1

see below

Explanation:

Package A

2n + 3m = 280

Package B

2n + 5m = 320

Using elimination to eliminate n since the coefficient is the same

Subtracting the A equation from the B equation

2n + 5m = 320

-2n - 3m = -280

------------------------

2m = 40

Divide by 2

2m/2 = 40/2

m = 20

Now finding n

2n+3m = 280

2n +3(20) = 280

2n+60 = 280

Subtract 60 from each side

2n +60-60= 280-60

2n = 220

Divide by 2

2n/2 = 220/2

n = 110

The cost per night is 110 and the cost per meal is 20