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A home designer will carpet n rooms wit...

A home designer will carpet n rooms with the same dimensions in a house using a specific type of carpeting. The designer charges using the expressions nClw, where n is the number of rooms, C is a constant with units of dollars per square meter. L is the length of the each room in meters, and w is the width of each room in meter. If a customer asks the designer to use a less expansive type oof carpating, which of the following factors in the expressions would change?

A

`n`

B

`C`

C

`l`

D

`w`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the expression given for the designer's charges, which is \( nClw \). Here, \( n \) is the number of rooms, \( C \) is a constant representing the cost per square meter of carpeting, \( L \) is the length of each room, and \( w \) is the width of each room. ### Step-by-Step Solution: 1. **Identify the Variables**: - \( n \): Number of rooms (constant) - \( C \): Cost per square meter (can change) - \( L \): Length of each room (constant) - \( w \): Width of each room (constant) 2. **Consider the Impact of Changing Carpeting**: - The question states that the customer wants to use a less expensive type of carpeting. This implies that the cost per square meter, represented by \( C \), is likely to change. 3. **Evaluate Each Factor**: - **Number of Rooms (\( n \))**: This will remain constant regardless of the type of carpeting chosen. The number of rooms does not change with the type of carpet. - **Length of Each Room (\( L \))**: This is a physical dimension of the room and will not change with the type of carpeting. - **Width of Each Room (\( w \))**: Similar to length, this is also a physical dimension and will remain constant. 4. **Conclusion**: - The only factor that can change when switching to a less expensive type of carpeting is \( C \), the cost per square meter. ### Final Answer: The factor that would change is \( C \) (the cost per square meter of carpeting). ---
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