MATH SOLVE

4 months ago

Q:
# A rectangular lot whose perimeter is 380 ft is fenced along three sides. An expensive fencing along the lot's length cost $ 25 per foot. An inexpensive fencing along the two side widths costs only $ 5 per foot. The total cost of the fencing along the three sides comes to $ 3625. What are the lot's dimensions?

Accepted Solution

A:

We have two widths of the same length plus one length

Let the width be [tex]w[/tex] and the length be [tex]l[/tex]

Perimeter = 2×width + 2×length

[tex]380 = 2w + 2l[/tex]

[tex]380 = 2(w+l)[/tex]

[tex]190 = w+l[/tex](equation 1)

The cost is $5 per foot on the width and $25 per foot on the length

Total cost = (5 × 2 × width) + (25 × length)

[tex]3625 = 10w + 25l[/tex] (equation 2)

We have two variables that we need to solve, so we will need to use the simultaneous equations method (either elimination or substitution)

Since equation 1 is given [tex]190 = w + l[/tex], we can rearrange the equation to make [tex]l[/tex] the subject

[tex]l=190-w[/tex]

then substitute this into equation 2

[tex]3625 = 10w + 25l[/tex]

[tex]3625=10w + 25(190-w)[/tex]

[tex]3625=10w+4750-25w[/tex]

[tex]3625=-15w+4750[/tex]

[tex]15w = 4750 - 3625[/tex]

[tex]15w = 1125[/tex]

[tex]w = 1125/15[/tex]

[tex]w = 75[/tex]

Substitute w = 75 back into 190 = w + l

190 = 75 + l

l = 190 - 75

l = 115

Answer:

Length = 115 feet

Width = 75 feet

Let the width be [tex]w[/tex] and the length be [tex]l[/tex]

Perimeter = 2×width + 2×length

[tex]380 = 2w + 2l[/tex]

[tex]380 = 2(w+l)[/tex]

[tex]190 = w+l[/tex](equation 1)

The cost is $5 per foot on the width and $25 per foot on the length

Total cost = (5 × 2 × width) + (25 × length)

[tex]3625 = 10w + 25l[/tex] (equation 2)

We have two variables that we need to solve, so we will need to use the simultaneous equations method (either elimination or substitution)

Since equation 1 is given [tex]190 = w + l[/tex], we can rearrange the equation to make [tex]l[/tex] the subject

[tex]l=190-w[/tex]

then substitute this into equation 2

[tex]3625 = 10w + 25l[/tex]

[tex]3625=10w + 25(190-w)[/tex]

[tex]3625=10w+4750-25w[/tex]

[tex]3625=-15w+4750[/tex]

[tex]15w = 4750 - 3625[/tex]

[tex]15w = 1125[/tex]

[tex]w = 1125/15[/tex]

[tex]w = 75[/tex]

Substitute w = 75 back into 190 = w + l

190 = 75 + l

l = 190 - 75

l = 115

Answer:

Length = 115 feet

Width = 75 feet