Question

a ski chalet offers 2 weekend packages. one package provides 2 nights and 3 meals for$280. the other provides 2 nights and 5 meals for $320. write and solve a system of equations to find the cost per night and per meal.

Answer 1

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