Question

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?

Answer 1

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.