College

Joe has 220 feet of material for the perimeter of the sandbox. If [tex]l[/tex] is the length of the sandbox and [tex]w[/tex] is the width, which system of equations represents this situation?

A. [tex]2w + l = 220[/tex]
[tex]w + 5 = 2l[/tex]

B. [tex]2w + l = 220[/tex]
[tex]w - 2l = 5[/tex]

C. [tex]2w + 2l = 220[/tex]
[tex]l = 2(w + 5)[/tex]

D. [tex]2w + 2l = 220[/tex]
[tex]l = 2w + 5[/tex]

Answer :

To solve this problem, we need to correctly represent the situation of the sandbox’s perimeter using a system of equations.

1. Understanding the Perimeter Equation:
- The perimeter [tex]\( P \)[/tex] of a rectangle is given by the formula [tex]\( P = 2w + 2l \)[/tex], where [tex]\( w \)[/tex] is the width and [tex]\( l \)[/tex] is the length.
- According to the problem, the perimeter is 220 feet. Therefore, the first equation representing this is:
[tex]\[
2w + 2l = 220
\][/tex]

2. Understanding the Relationship between Length and Width:
- We are given a specific relationship between the length and width in the problem statement. This relationship is:
- The length [tex]\( l \)[/tex] is related to the width [tex]\( w \)[/tex] by the equation [tex]\( l = 2w + 5 \)[/tex].
- This becomes our second equation:
[tex]\[
l = 2w + 5
\][/tex]

3. Forming the System of Equations:
- With these two equations established:
1. [tex]\( 2w + 2l = 220 \)[/tex] (perimeter equation)
2. [tex]\( l = 2w + 5 \)[/tex] (relationship between length and width)
- We see that these are the equations that form the system we need.

Thus, the correct choice that represents this situation is option D:
[tex]\[
2w + 2l = 220
\][/tex]
[tex]\[
l = 2w + 5
\][/tex]

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