Q 110 - Intermediate Algebra

Question

A frame around a family portrait has a perimeter of $90$ inches. The length is fifteen less than twice the width. Find the length and width of the frame.

Step-by-Step Solution

Answer

The length and width of the frame are $25$ and $20$ inches respectively.

Step 1 Given information is,

A frame around a family portrait has a perimeter of $90$ inches.

The length is  fifteen less than twice the width. Find the length and width of the frame.

Step 2 To find:

The length and width of the frame.

Step 3 Let us consider,

$l$ represents the length of the frame.

$w$ represents the width of the frame.

It is given that,frame around a family portrait has a perimeter of $90$ inches.

From the above lines, the obtained equation is,$$\begin{gathered} 2\left(l+w\right)=90 \\ l+w=\frac{90}{2} \\ l+w=45 \end{gathered}$$

The length is fifteen less
than twice the width. 

So, $l=2w-15$

Step 4 From the step 3 ,

The obtained linear equations are,

$$\begin{gathered} l+w=45 \\ l=2w-15 \end{gathered}$$

Now substitute $l=2w-15$ in the equation $l+w=45$.

$$\begin{gathered} 2w-15+w=45 \\ -15+3w=45 \\ 3w=45+15 \\ 3w=60 \\ w=\frac{60}{3} \\ w=20 \end{gathered}$$

Step 5 Find the value of l .

Substitute the value of $w$ in the equation $l+w=45$.

$$\begin{gathered} l+20=45 \\ l=45-20 \\ l=25 \end{gathered}$$