Question

Part I: The equation representing package A is given. Complete the system of equations by writing an equation to represent package B. (1 point)

Answer:
Package A: 2n + 3m = 280
Package B: Question Blank 1 of 1
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)
Step 4: Explain the meaning of the solutions for m and n. (2 points: 1 point each)

Answer 1

Part I — Answers

1) Equation for package B:
2n + 5m = 320

2) Method chosen:
Elimination. Reason: Both equations have the same coefficient for n (2), so subtracting one equation from the other immediately eliminates n.

3) Solve the system (showing work):

Given:
2n + 3m = 280
2n + 5m = 320

Subtract the first equation from the second:
(2n + 5m) − (2n + 3m) = 320 − 280
2m = 40
m = 20

Substitute m = 20 into 2n + 3m = 280:
2n + 3(20) = 280
2n + 60 = 280
2n = 220
n = 110

So n = 110 and m = 20.

4) Meaning of the solutions:
- n = 110 means one night costs $110 (or 110 units of currency).
- m = 20 means one meal costs $20 (or 20 units of currency).