Translating to algebraic expressions

[NotaMathPerson]

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?

 

[Deveno]

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 $3$).

 

[NotaMathPerson]

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?

 

[MarkFL]

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 $\ell$:

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