Q 111 - Intermediate Algebra

Question

The perimeter of a toddler play area is $100$ feet. The length is ten more than three times the width. Find the length and width of the play area.

Step-by-Step Solution

Answer

The length and width of the play area are $40$ and $10$ feet respectively.

Step 1 Given information is,

The perimeter of a toddler play area is $100$ feet. 

The length is ten more than three times the width.

Step 2 To find:

The length and width of the play area.

Step 3 Let us consider,

$l$ represents the length of the play area.

$w$ represents the width of the play area.

The perimeter of a toddler play area is $100$ feet.

From the above lines the obtained equation is,

 $$\begin{gathered} 2\left(l+w\right)=100 \\ l+w=50 \end{gathered}$$

The length is ten more than three times the width. 

So,$l=10+3w$.

Step 4 From the step 3 ,

The obtained linear equations are,

$$\begin{gathered} l+w=50 \\ l=10+3w \end{gathered}$$

Now substitute $l=10+3w$ in the equation $l+w=50$.

$$\begin{gathered} 10+3w+w=50 \\ 10+4w=50 \\ 4w=50-10 \\ 4w=40 \\ w=\frac{40}{4} \\ w=10 \end{gathered}$$

Step 5 Find the value of l .

Now substitute the value of $w$ in the equation $l+w=50$.

$$\begin{gathered} l+10=50 \\ l=50-10 \\ l=40 \end{gathered}$$