The perimeter of a rectangular deck is 175 feet. The length of the deck, L, is 6 feet longer than 2 times the width, W. Which system of equations can be solved to determine the length and width, in feet, of the deck? What is the correct formula and why?
a) 2L+2W=175
L=2-6W
b) 2L+2W=175
L=2W-6
c) 2L+2W=175
L=6-2W
d) 2L+2W=175
L=6+2W
c) 2l+2w=175
l
2L+2W=175
L=6+2W
Answer d)
Oh it looks like you have five options! Let me go through them and see which one is correct.
a) 2L+2W=175, L=2-6W
Hmm, this equation seems a bit odd. The length of the deck is expressed as 2-6W, but we want it in terms of W. This doesn't look right.
b) 2L+2W=175, L=2W-6
Okay, this equation seems a bit more logical. The length of the deck is expressed as 2W-6, which is 2 times the width minus 6. So this one is a possible option.
c) 2L+2W=175, L=6-2W
Wait a second, this equation seems like it's trying to calculate the length using the width, but in a slightly different way. The width is subtracted from 6, instead of being subtracted from the length. This doesn't seem correct.
d) 2L+2W=175, L=6+2W
Hmm, this equation seems similar to option b. The length of the deck is expressed as 6+2W, which is 6 plus 2 times the width. This could be a possible option as well.
e) 2L+2W=175, L
Hmm, it looks like there is a missing equation here. We need an equation to solve for the length of the deck.
Based on the options provided, I would say that option b) is the most suitable equation to determine the length and width of the deck. The formula 2L + 2W = 175 is the correct perimeter formula for a rectangular deck, and L = 2W-6 seems to represent the relationship between the length and width.
The correct system of equations to determine the length and width of the deck is:
a) 2L + 2W = 175
L = 2W - 6
We can derive this system of equations from the information given.
First, let's assign variables to the length and width of the deck. Let L represent the length and W represent the width.
The perimeter of a rectangle is calculated by adding up all four sides. In this case, the perimeter is given as 175 feet.
The formula for the perimeter of a rectangle is 2L + 2W, which represents the sum of the lengths of two opposite sides (2L) and the sum of the widths of the other two sides (2W).
So, the first equation is 2L + 2W = 175. This equation represents the relationship between the length and width that gives the perimeter of the rectangle.
The second equation comes from the given information that the length (L) is 6 feet longer than 2 times the width (W).
This can be written as L = 2W + 6.
However, looking at the options provided, we see that the equation given is L = 2W - 6. This is because if we rearrange the equation L = 2W + 6, we get L - 6 = 2W, which implies W = (L - 6)/2.
So, we need to rewrite the equation to match the given format, which is L = 2W - 6.
Therefore, the correct system of equations to determine the length (L) and width (W) of the deck is:
a) 2L + 2W = 175
L = 2W - 6
Let's break down the information given in the problem.
1. The perimeter of a rectangular deck is 175 feet.
The formula for the perimeter of a rectangle is given by 2L + 2W, where L is the length and W is the width.
2. The length of the deck, L, is 6 feet longer than 2 times the width, W.
This can be expressed as L = 2W + 6.
Now, let's compare the given options with the information we derived:
a) 2L + 2W = 175, L = 2 - 6W
b) 2L + 2W = 175, L = 2W - 6
c) 2L + 2W = 175, L = 6 - 2W
d) 2L + 2W = 175, L = 6 + 2W
Looking at the options, we can eliminate options a) and b) because the equation L = 2 - 6W in option a) and L = 2W - 6 in option b) do not match the given information L = 2W + 6.
Now, let's evaluate options c) and d).
c) 2L + 2W = 175, L = 6 - 2W
If we substitute L = 6 - 2W into the equation 2L + 2W = 175:
2(6 - 2W) + 2W = 175
12 - 4W + 2W = 175
12 - 2W = 175
-2W = 175 - 12
-2W = 163
W = 163 / -2
W = -81.5
Since we have obtained a negative value for the width, this solution is not valid.
d) 2L + 2W = 175, L = 6 + 2W
If we substitute L = 6 + 2W into the equation 2L + 2W = 175:
2(6 + 2W) + 2W = 175
12 + 4W + 2W = 175
12 + 6W = 175
6W = 175 - 12
6W = 163
W = 163 / 6
W ≈ 27.17
Since we have obtained a decimal value for the width, this solution is also not valid.
Therefore, none of the options a), b), c), or d) can be solved to determine the length and width of the deck. There might be an error in the given options, or the question might require additional information to find a valid solution.