Questions: Joe plans to put a swing set inside a sand box 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. 2w + l = 220, w = 2l + 5 B. 2w + 2l = 220, l = 2v C. 2w + 2l = 220 D. w + l = 220, 2 + 5 = 2l

Solution Steps

Joe needs to build a sandbox with a specific length and width. The length \( l \) should be 5 feet longer than twice the width \( w \). Additionally, he has 220 feet of material for the perimeter of the sandbox.

1. Perimeter Equation: The perimeter \( P \) of a rectangle is given by \( P = 2w + 2l \). Since Joe has 220 feet of material, the equation becomes: \[ 2w + 2l = 220 \]
2. Length-Width Relationship: The length \( l \) is 5 feet longer than twice the width \( w \). This can be written as: \[ l = 2w + 5 \]

Now, we compare the derived equations with the given options:

• Option A: \[ \left\{\begin{array}{c}2 w+l=220 \\ w=2 l+5\end{array}\right. \] This does not match our equations.

• Option B: \[ \left\{\begin{array}{l} 2 w+2 l=220 \\ l=2 w+5\end{array}\right. \] This matches our derived equations.

• Option C: \[ \left\{\begin{array}{l} 2 w+2 l=220 \\ l=2 w+5\end{array}\right. \] This is identical to Option B and also matches our equations.

• Option D: \[ \left\{\begin{array}{l} w+l=220 \\ l=2 w+5\end{array}\right. \] This does not match our equations.

Final Answer