Question

A ski lodge offers two weekend packages. Package A provides 2 night 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.
Step 1: The equation representing package A is given. Complete the system of equations by writing an equation to represent package B.
Package A: 2n + 3m = 280
Packkage 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)
Step 5: Write like a 9th grader and also be sure not to talk too much, just use the words: So then, then, equals, therefore, add, get rid of, after this.

Answer 1

Step 1:
Package B: 2n + 5m = 320

Step 2:
Method: elimination — I chose elimination because both equations have 2n, so you can add or subtract to get rid of n.

Step 3 (work):
So then subtract A from B: (2n + 5m) - (2n + 3m) = 320 - 280
So then 2m equals 40, then m equals 20.
after this substitute m into A: 2n + 3(20) = 280
2n + 60 = 280 then get rid of 60 by subtracting 60: 2n = 220
then divide by 2 therefore n equals 110

Step 4 (meaning):
m equals $20 — each meal costs $20.
n equals $110 — each night costs $110.