Choice A: 3 nights and one meal for $ 250

Choice B: 3 nights and 6 meals for $330

A motel offers the specials shown. What price is the motel charging per night?

N = number of nights

M = number of meals

n = cost per night

m = cost per meal

T = total cost

Nn + Mm = T

They give us two scenarios:

1. N = 3 and M = 1 and T = 250

3n + 1m = 250

2. N = 3 and M = 6 and T = 330

3n + 6m = 330

Thus, we have a system of equations.

In the first equation, solve for m.

m = 250 - 3n

Now, plug this into the second equation and solve for n.

3n + 6m = 330

3n + 6 (250 - 3n) = 330

3n + 1500 - 18n = 330

-15n = - 1170

n = $78

Now, plug this back into our equation for m and solve.

m = 250 - 3n

m = 250 - 3 (78)

m = 250 - 234

m = $16

Thus, it costs $78 per night and $16 per meal.