Word problem, need help!

[IBMguy]

Ok math gurus, here's something that has been wrecking my brain. I have this word problem listed here:

"A rectangular lot whose perimeter is 320 feet is fenced along THREE sides. An expensive fencing along the lot's length costs $20 per foot and an inexpensive fencing costs $8 per foot. The total cost of the fencing along the three sides comes to $5800. What are the lot's dimensions?"

I know that:
W=Width
L=Length

and on one of the equations is:
L + 2W = 320 (Divide by 2)
L + W = 160

But I'm stuck there trying to figure the rest of the problem out.

 

[Deleted member 4993]

Ok math gurus, here's something that has been wrecking my brain. I have this word problem listed here:

"A rectangular lot whose perimeter is 320 feet is fenced along THREE sides. An expensive fencing along the lot's length costs $20 per foot and an inexpensive fencing costs $8 per foot. The total cost of the fencing along the three sides comes to $5800. What are the lot's dimensions?"

I know that:
W=Width
L=Length

and on one of the equations is:
L + 2W = 320 (Divide by 2)..........................................(1)
L + W = 160 <<<<< How did you get that? You could write L/2 + W = 160 --- but that is not very helpful

But I'm stuck there trying to figure the rest of the problem out.

Then you have:

20 * L + 8*(2*W) = 5800 ............................................(2)

Now you have two equations and two unknowns.

What method/s do you know to solve such system of equation?

 

[IBMguy]

Subhotosh:

I can use either substitution or elimination methods.

So L + W = 160 is incorrect then?

 

[IBMguy]

To further illustrate, I will post what I have done so far:

L + 2W = 320 (Divide by 2)
L + W = 160
Subtracting W from both sides leaves the equation:
L = 160 – W. We will call this Equation 1.
We know from the cost side that 1 length x 20 dollars per foot and 2X widths at 8 dollars per foot = $5800.
Therefore 20L + 8W + 8W = 5800, we shall call this Equation 2.However, we know from Equation 1 that L = 160 – W, therefore, we substitute this value (160-W) for L in Equation 2, which then becomes:
20(160-W) + 8W + 8W = 5800

​

 

[srmichael]

To further illustrate, I will post what I have done so far:

L + 2W = 320 (Divide by 2)
L + W = 160
Subtracting W from both sides leaves the equation:
L = 160 – W. We will call this Equation 1.
We know from the cost side that 1 length x 20 dollars per foot and 2X widths at 8 dollars per foot = $5800.
Therefore 20L + 8W + 8W = 5800, we shall call this Equation 2.However, we know from Equation 1 that L = 160 – W, therefore, we substitute this value (160-W) for L in Equation 2, which then becomes:
20(160-W) + 8W + 8W = 5800

​

No, no, no, no, no.

L + 2W = 320 does NOT simplify to L + W = 160 as Subhotosh Kahn already mentioned. He also mentioned that you now have two equations and two unknowns, thus solvable.

1) L + 2w = 320
2) 20L + 16W = 5800

This is all you need to solve. Now proceed....