Hi there!
Important information we know:
Fencing costs $48 per yard (1 yard = $48)
Width : X
Length : 4X - 250
Total cost of fencing : $24,000
Steps to finding the answer:
1. First off, you'll need to find how many yards the fencing is (the perimeter of the fencing). To do so, You need to use the cross product method with the information you know about the cost of the fencing per yard and the total cost of the fencing :
1 yard fencing = $48
? yards fencing = $24,000
(1 × 24,000) ÷ 48 = ? yards fencing
24,000 ÷ 48 = ? yards fencing
500 = ? yards fencing
This means that the perimeter of the fencing is 500 yards.
2. Now that you have the perimeter of the fencing, you'll need to use the general formula of the perimeter of a rectangle and replace all the information you have in it (I'm guessing that the fencing is in a rectangular shape because it's the most common shape and that the information is not mentionned) :
P = (Length × 2) + (Width × 2)
P = 500
Length = 4X - 250
Width = X
500 = ((4X - 250) × 2) + (X × 2)
3. Now that you have your equation, all you need to do next is to solve it by isolating "x" to find the width :
500 = ((4X - 250) × 2) + (X × 2)
(4X - 250) × 2 = (4X × 2) + (-250 × 2)
4X × 2 = 8X
-250 × 2 = -500
(4X - 250) × 2 = 8X - 500
(X × 2) = 2X
500 = 8X - 500 + 2X
Add 500 to each side of the equation → 500 + 500 = 1,000
1,000 = 8X + 2X
Add similar terms together → 8X + 2X = 10X
1,000 = 10X
Divide each side of the equation by 10 → 1,000 ÷ 10 = 100
100 = X → The width of his fencing is 100 yards.
4. Now that you know the width of the fencing, you just need to replace the "X" in the length in order to find its measure :
Length = 4X - 250
Length = 4(100) - 250
Length = 400 - 250
Length = 150 → The length of his fencing is 150 yards.
There you go! I really hope this helped, if there's anything just let me know! :)
