MHB Translating to algebraic expressions

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To determine the amount of carpet needed for a room, the area of the room in square yards is calculated as A_R = px/3. Each yard of carpet, which is 2 ft wide, covers an area of A_C = 2ℓ/3 in square yards. By equating the two areas, the equation px/3 = 2ℓ/3 is established. Solving for ℓ yields ℓ = px/2, which indicates the minimum length of carpet required. This solution aligns with the book's answer, confirming the calculations.
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I am not able to express it symbolically I need your assistance. Thanks!

A room is $p$ ft. Long and $x$ yards in width; how many yards of carpet two ft. Wide will be required for the floor?
 
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One yard is 3 feet, so each yard of carpet covers 6 square feet. Your total area is $\dfrac{px}{3}$ square feet.

So if $y$ is the number of yards of carpet, you need to solve for $y$ in:

$6y = \dfrac{px}{3}$, to get the minimum needed (it could be more if neither $p$ nor $\dfrac{x}{3}$ is evenly divisible by $2$ or $3$).
 
Deveno said:
One yard is 3 feet, so each yard of carpet covers 6 square feet. Your total area is $\dfrac{px}{3}$ square feet.

So if $y$ is the number of yards of carpet, you need to solve for $y$ in:

$6y = \dfrac{px}{3}$, to get the minimum needed (it could be more if neither $p$ nor $\dfrac{x}{3}$ is evenly divisible by $2$ or $3$).

The answer in my book is
$\frac{px}{2}$

Why is that?
 
The area $A_R$ of the room in square yards is:

$$A_R=\frac{px}{3}$$

For a length $\ell$ of carpet in yards, its area $A_C$ in square yards is:

$$A_C=\frac{2\ell}{3}$$

Equating the two areas:

$$\frac{px}{3}=\frac{2\ell}{3}$$

Solve for $\ell$:

$$\ell=\frac{px}{2}$$
 
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