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

Answer:

1st formula 2n + 3m = 280

2nd formula 2n + 5m = 320

rearrange 1st formula to equal n:

   2n = -3m + 280

    n = -3/2 m + 140

rearrange 2nd formula to equal n:

2n = -5m + 320

n = -5/2m + 160

so now you have

-3/2m + 140 = -5/2m + 160

Rearrange to become:

-3/2m + 5/2m = 160 - 140

m = 20

Now place 20 into the very 1st equation in place of the letter m

2n + 3(20) = 280

2n + 60 = 280

2n = 220

n = 110

so it costs $110 per night, $20 per meal