Q 109 - Intermediate Algebra

Question

Darrin is hanging $200$ feet of Christmas garland on the three sides of fencing that enclose his front yard. The length is five feet less than three times the width. Find the length and width of the fencing.

Step-by-Step Solution

Answer

The length and the width of the fencing are $118$and $41$ feet respectively.

Step 1 Given information is,

Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that encloses his front yard. The length is five feet less than three times the width.

Step 2 To find:

The length and width of the fencing.

Step 3 Let us consider,

$l$ represents the length of the fencing.

$w$ represents the width of the fencing.

It is given that, Darrin is hanging $200$ feet of Christmas garland on the three sides of fencing that enclose his front yard.

The above lines give an equation,$l+2w=200$

The length is five feet less than three times the width.

So, $l=3w-5$.

Step 4 From the step 3 ,

The obtained linear equations are,

$$\begin{gathered} l+2w=200 \\ l=3w-5 \end{gathered}$$

Now substitute $l=3w-5$ in the equation $l+2w=200$.

$$\begin{gathered} 3w-5+2w=200 \\ -5+5w=200 \\ 5w=200+5 \\ 5w=205 \\ w=\frac{205}{5} \\ w=41 \end{gathered}$$

Step 5 find the value of l .

Substitute the value of $l$ in the equation.

$$\begin{gathered} l=3\left(41\right)-5 \\ l=123-5 \\ l=118 \end{gathered}$$