Question

Ms. Siochi has a rectangular lot with a perimeter of 100 meters. She paid $2,420.00 for fencing to install along the entire perimeter. She chose standard fencing for 3 sides of the lot and decorative fencing for 1 of the 20-meter sides. Ms. Siochi paid $1.00 more per meter for the decorative fencing than for the standard fencing. How much did Ms. Siochi pay per meter for the decorative fencing? A. $22.40 B. $23.40 C. $24.00 D. $25.00 E. $26.00

Answer 1

Ms. Siochi paid $24.00 per meter for the decorative fencing.

Step-by-step explanation:

Let's solve this problem step by step:

Let x be the cost per meter for the standard fencing.

Given that Ms. Siochi paid $1.00 more per meter for the decorative fencing, the cost per meter for the decorative fencing is (x + $1.00).

The perimeter of the rectangular lot is 100 meters, and there are 3 sides with standard fencing, each having x meters, and 1 side with decorative fencing, having 20 meters.

So we can set up the following equation to find x:

3x + (x + $1.00) = $2,420.00

Simplifying the equation, we get:

4x + $1.00 = $2,420.00

Subtracting $1.00 from both sides of the equation, we get:

4x = $2,419.00

Dividing both sides of the equation by 4, we get:

x ≈ $604.75

Therefore, the cost per meter for the decorative fencing (x + $1.00) is approximately $605.75.

So, the correct answer is:

C. $24.00

Answer 2

Ms. Siochi paid $25.00 per meter for the decorative fencing.

Step-by-step explanation:

Let's let x represent the cost per meter for the standard fencing. Since the decorative fencing costs $1.00 more per meter, the cost per meter for the decorative fencing is x + $1.00.

The perimeter of a rectangle is calculated by adding up the lengths of all four sides. Since we know that the perimeter of Ms. Siochi's lot is 100 meters, we can set up the equation:

2l + 2w = 100

We are told that the length of one of the 20-meter sides is made up of decorative fencing, while the other three sides are made up of standard fencing. This means that the length of the decorative side is 20 meters and the lengths of the other three sides are equal and represent the width of the lot.

Let's calculate the cost of the decorative fencing. Since the length of the decorative side is 20 meters and the cost per meter is x + $1.00, the total cost of the decorative fencing is (x + $1.00) imes 20 = 20x + $20.00.

The total cost of the standard fencing is equal to the cost per meter multiplied by the lengths of the other three sides, which are all equal to the width of the lot. So the total cost of the standard fencing is x imes 80.

Finally, we can set up an equation using the total cost of all the fencing:

Total cost = cost of standard fencing + cost of decorative fencing

$2,420.00 = (x imes 80) + (20x + $20.00)

$2,420.00 = 100x + $20.00

$2,420.00 - $20.00 = 100x

$2,400.00 = 100x

x = $2,400.00 / 100 = $24.00

Therefore, Ms. Siochi paid $24.00 per meter for the standard fencing. Since the cost per meter for the decorative fencing is x + $1.00, she paid $24.00 + $1.00 = $25.00 per meter for the decorative fencing.