Question

1) A hotel is offering the two weekend specials described below.
Plan 1: 3 nights and 4 meals for $233
Plan 2: 3 nights and 3 meals for $226.50
For accounting purposes, the hotel will record the income for the stay and the meals separately. So the cost per night for each special must be the same.
a. what is the system of equations for this situation?
b. solve the system. what is the cost per night and cost per meal?

Answer 1

@SeaTurtle113 could you help?

Answer 2

3n + 4m = 233 -- >(-1) 3n + 4m = 233
3n + 3m = 226.50
-----------------
-3n - 4m = -233 (result of multiplying by -1)
3n + 3m = 226.50
----------------add
-m = -6.50
m = 6.50
now sub 6.50 in for m in either equation...
3n + 4m = 233
3n + 4(6.50) = 233
3n + 26 = 233
3n = 233 - 26
3n = 207
n = 207/3
n = 69
check...
3n + 3m = 226.5
3(69) + 3(6.5) = 226.50
207 + 19.50 = 226.50
226.50 = 226.50 (correct)
ANSWER : cost per night (n) = $ 69.00
cost per meal (m) = $ 6.50

Answer 3

Thank you!

Answer 4

My pleasure!