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Direct Variation Word Problem: Tiling Cost and Room Size Calculation
Published on December 1, 2025
Word-Problem
Solve a direct variation problem involving the cost of tiling a room based on its size. Calculate the size of a kitchen given its tiling cost and the cost per square foot.
Question
Answer
The problem states that the price of tiling a room varies directly as the size of the room. This means that the ratio of the price to the size of the room is constant.
Let
According to the problem,
This can also be written as
According to the problem,
This can also be written as
We are given that the tiling costs $4,224.00 for 264 square feet.
So, we can find the constant
So, we can find the constant
Now, we need to find the size of a kitchen that costs $3,824.00. Let this size be
We can set up a proportion:
We can set up a proportion:
Given:
Substitute the given values into the proportion:
To solve for
Now, calculate the product on the right side:
So, the equation becomes:
Divide both sides by 4224 to find
So, the size of the kitchen that costs $3,824.00 is 239 square feet.
Let’s check the options:
A. 239 square feet
B. 7,648 square feet
C. 63,096 square feet
D. 256 square feet
A. 239 square feet
B. 7,648 square feet
C. 63,096 square feet
D. 256 square feet
Our calculated value matches option A.
The final answer is