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

3n + m = 250 -- (3 nights(n) + 1 meal (m) = 250) --- multiply by -1
3n + 6m = 330 -- (3 nights + 6 meals = 330)
---------------------
-3n -m = -250 (result of multiplying by -1)
3n + 6m = 330
--------------------add
5m = 80
m = 80/5
m = 16

now sub 16 in for n in either of the original equations
3n + m = 250
3n + 16 = 250
3n = 250 - 16
3n = 234
n = 234/3
n = 78

check..
3n + 6m = 330
3(78) + 6(16) = 330
234 + 96 = 330
330 = 330 (correct)

so each night (n) costs $ 78