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 income for the stay and the meals separately. So the cost per night for each special must be the same, and the cost per meal for each special must be the same.
a. What is a system of equations for the situation?
b. Solve the system. What is the cost per night and the cost per meal?
a.
To write the system of equations for the given situation
Answer to Problem 6STP
Explanation of Solution
Given:
An hotel offers the 2 plans, i.e.,
Plan 1: 3 nights and 4 meals for $233
Plan 2: 3 nights and 3 meals for $226.50
Formula Used:
Calculation:
Let,
The Cost of per night be $
The Cost of per meal be $
Given,
Plan 1: 3 nights and 4 meals for $233
Therefore,
Also,
Plan 2: 3 nights and 3 meals for $226.50
Therefore,
Conclusion:
Hence, the required system of equations is:
b.
To solve the system of equation obtained in the previous part
Answer to Problem 6STP
Cost of per night is $ 69
Cost of per meal is $ 6.5
Explanation of Solution
The obtained system of equations is:
Calculation:
Let,
Now, subtract equation (ii) and ( i ),
Substituting the value of
Conclusion:
Hence, cost of per night is $ 69 and cost of per meal is $ 6.5.
Chapter 6 Solutions
High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
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