Select the correct answer.

Joe plans to put a swing set inside a sandbox he is building in his yard. He needs the sandbox to be 5 feet longer than twice the width for safety purposes. Joe has 220 feet of material that he will use for the perimeter of the sandbox. If \( l \) is the length of the sandbox and \( w \) is the width, which system of equations represents this situation?

A. \(\left\{\begin{array}{c}2 w+2 l=220 \\ l=2(w+5)\end{array}\right.\)

B. \(\left\{\begin{array}{l}w+l=220 \\ w+5=2 l\end{array}\right.\)

C. \(\left\{\begin{array}{c}2 w+2 l=220 \\ l=2 w+5\end{array}\right.\)

D. [tex]\(\left\{\begin{array}{c}2 w+l=220 \\ w=2 l+5\end{array}\right.\)[/tex]



Answer :

To determine the correct system of equations that represents the given situation, we need to translate the problem's conditions into mathematical equations.

1. We are told that the length of the sandbox (denoted by \( l \)) is 5 feet longer than twice the width (denoted by \( w \)). This translates into the equation:
[tex]\[ l = 2w + 5 \][/tex]

2. We also know that the total perimeter of the sandbox is 220 feet. The perimeter of a rectangle is given by the formula \( 2w + 2l \), which leads to the equation:
[tex]\[ 2w + 2l = 220 \][/tex]

Now, putting these two equations together to form a system of equations, we have:
[tex]\[ \left\{ \begin{array}{c} 2w + 2l = 220 \\ l = 2w + 5 \end{array} \right. \][/tex]

Looking at the provided options, this system of equations corresponds to option C:
[tex]\[ \left\{ \begin{array}{c} 2w + 2l = 220 \\ l = 2w + 5 \end{array} \right. \][/tex]

Therefore, the correct answer is [tex]\( \boxed{C} \)[/tex].