4. 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.

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
package b:

step 2: select a method for solving the system. which method did you choose? why?

step 3: solve the system of equations to find the costs per night and per meal. show your work.

step 4: explain the meaning of the solutions for m and n.