Question
The length of a garden plot is 3 yards less than 2 times the width. Which equation describes the relationship between the width `w` of the plot in yards, and the area `A` in square yards?
Answers
GPT-4o mini
To express the relationship between the width `w` of the garden plot and its area `A`, we first need to establish the dimensions based on the information provided.
Given that the length \( l \) of the garden plot is "3 yards less than 2 times the width", we can express the length as:
\[
l = 2w - 3
\]
Next, the area \( A \) of a rectangle (which describes the garden plot) is calculated as the product of its length and width:
\[
A = l \times w
\]
Substituting our expression for \( l \) into the area formula:
\[
A = (2w - 3) \times w
\]
Now, we can expand this equation:
\[
A = 2w^2 - 3w
\]
Thus, the equation that describes the relationship between the width \( w \) of the plot in yards and the area \( A \) in square yards is:
\[
A = 2w^2 - 3w
\]
Given that the length \( l \) of the garden plot is "3 yards less than 2 times the width", we can express the length as:
\[
l = 2w - 3
\]
Next, the area \( A \) of a rectangle (which describes the garden plot) is calculated as the product of its length and width:
\[
A = l \times w
\]
Substituting our expression for \( l \) into the area formula:
\[
A = (2w - 3) \times w
\]
Now, we can expand this equation:
\[
A = 2w^2 - 3w
\]
Thus, the equation that describes the relationship between the width \( w \) of the plot in yards and the area \( A \) in square yards is:
\[
A = 2w^2 - 3w
\]