Solving for Hotel Room Availability: A Comprehensive Algebraic Approach

The question at hand involves determining the total number of rooms in a hotel given certain conditions about the occupancy and reservations. Let's explore the problem step-by-step, using algebraic equations to find the solution.

Problem Description

The problem states: '3/5 of rooms in a hotel are occupied. 22 rooms are also reserved. 127 rooms in total are unavailable. How many rooms are in the hotel?'

Algebraic Formulation

We will denote the total number of rooms in the hotel as x. According to the problem, we have the following information:

occupied rooms: frac{3}{5} of the rooms are occupied, which means the number of occupied rooms is frac{3}{5}x. reserved rooms: There are 22 rooms reserved. unavailable rooms: The total number of unavailable rooms, which includes both occupied and reserved, is 127.

Setting Up the Equation

We can set up the following equation based on the information provided:

occupied rooms reserved rooms unavailable rooms

Substituting the values we have:

frac{3}{5}x 22 127

Solving for x

To solve for x, we need to follow these steps:

Subtract 22 from both sides: frac{3}{5}x 105 Multiply both sides by the reciprocal of frac{3}{5}, which is frac{5}{3} to isolate x: x 105 * frac{5}{3} x 175

Thus, the total number of rooms in the hotel is 175.

Summary of the Algebraic Equation

frac{3}{5}x   22  127

Final Answer

The total number of rooms in the hotel is 175.

Further Considerations

While solving the problem using algebra, it is important to also consider the context in which this question is posed. For example, we should consider:

Is there cultural and economic class bias? Do all students have an understanding of hotel operations? Are there students from backgrounds where hotel stays are unfamiliar, thus the question may feel less fair?

These questions should be addressed in future educational settings to ensure fairness and inclusivity.