A ski lodge offers 3 weekend packages. One package provides 2 nights, 3 meals and 1 ski lesson for $310. The second package provides 2 nights, 5 meals and 2 ski lessons for $380. The third package provides 1 night and two meals for $150. Write and solve a system of equations to find the cost per night, per meal, and per lesson. show your work.

The cost of 1 meal, 1 night and 1 ski lesson is $ 160.

Step-by-step explanation:

Let the nights be N , meals be M, ski lesson is S.

According to the question

2 N + 3 M + S = 310(1)

2 N + 5 M + 2 S = 380 (2)

N + 2 M = 150 (3)

By solving (1), (2) and (3) we get

N = $ 110, M = $ 20, S = $ 30

So, the cost of 1 night, 1 meal, 1ski lesson is

1 x 110 + 1 x 20 + 1 x 30

= 110 + 20 + 30

= $ 160