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Y_Kistochka [10]
3 years ago
8

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?
Mathematics
1 answer:
AlekseyPX3 years ago
7 0
We have two widths of the same length plus one length

Let the width be w and the length be l

Perimeter = 2×width + 2×length
380 = 2w + 2l
 380 = 2(w+l)
190 = w+l(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)
3625 = 10w + 25l (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 190 = w + l, we can rearrange the equation to make l the subject

l=190-w

then substitute this into equation 2

3625 = 10w + 25l
3625=10w + 25(190-w)
3625=10w+4750-25w
3625=-15w+4750
15w = 4750 - 3625
15w = 1125
w = 1125/15
w = 75

Substitute w = 75 back into 190 = w + l

190 = 75 + l
l = 190 - 75
l = 115

Answer:
Length = 115 feet
Width = 75 feet

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