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A painter will paint n walls with the sa...

A painter will paint n walls with the same size and shape in a building using a specific brand of paint. The painter’s fee can be calculated by the expression nKAh, where n is the number of walls, K is a constant with units of dollars per square foot, A is the length of each wall in feet, and h is the height of each wall in feet. If the customer asks the painter to use a more expensive brand of paint, which of the factors in the expression would change?

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Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the expression given for the painter's fee, which is \( nKAh \). Here, \( n \) is the number of walls, \( K \) is a constant representing the cost of paint per square foot, \( A \) is the length of each wall in feet, and \( h \) is the height of each wall in feet. ### Step-by-Step Solution: 1. **Identify the Variables**: - \( n \): Number of walls (unitless) - \( K \): Cost per square foot (dollars/square foot) - \( A \): Length of each wall (feet) - \( h \): Height of each wall (feet) 2. **Understand the Expression**: The expression \( nKAh \) calculates the total fee for painting \( n \) walls, where \( K \) is the cost associated with the paint used. 3. **Determine Which Factors Change with Paint Brand**: - The number of walls \( n \) does not change regardless of the paint brand. It is simply a count of how many walls are being painted. - The dimensions of the walls, \( A \) (length) and \( h \) (height), also remain constant as they are determined by the physical structure of the building and do not depend on the type of paint used. - The only factor that would change if a more expensive brand of paint is used is \( K \), the cost per square foot. This is because different brands of paint have different pricing, which directly affects the overall cost of painting. 4. **Conclusion**: Therefore, the factor in the expression \( nKAh \) that would change if the customer asks the painter to use a more expensive brand of paint is \( K \). ### Final Answer: The factor that would change is \( K \) (the cost per square foot of paint).
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