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Fencing costs $25.80 per yard. How much does it cost to enclose two adjacent rectangular pastures as shown?

Fencing costs $25.80 per yard. How much does it cost to enclose two adjacent rectangular pastures as shown?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Problem:** Fencing costs $25.80 per yard. How much does it cost to enclose two adjacent rectangular pastures as shown? **Diagram Description:** The image shows two adjacent rectangular pastures enclosed by a wooden fence. The dimensions of the pastures are given as follows: - The total length of the longer side, which covers both pastures, is \(50 \frac{5}{8}\) yards. - The length of the shorter side of each pasture is \(30 \frac{2}{9}\) yards. - There is no divider fence between the two pastures along the shorter side. **Solution Approach:** 1. Calculate the total amount of fencing needed. 2. Multiply the total length of fencing by the cost per yard to find the total cost. **Calculations:** - Total length of fencing includes the perimeter of the two rectangles minus the shared side. - Perimeter Calculation: - Total Length: \(50 \frac{5}{8}\) yards - Total Width: \(30 \frac{2}{9} \times 2\) (since there are two sections with the same width) - Total fencing needed = \(2 \times 50 \frac{5}{8} + 2 \times (30 \frac{2}{9}) - (30 \frac{2}{9})\). - Find the total cost by multiplying the total fencing length by $25.80. This problem involves calculating the perimeter of the fence required to enclose the described pastures and then determining the total cost using the given rate per yard.
Transcribed Image Text:**Problem:** Fencing costs $25.80 per yard. How much does it cost to enclose two adjacent rectangular pastures as shown? **Diagram Description:** The image shows two adjacent rectangular pastures enclosed by a wooden fence. The dimensions of the pastures are given as follows: - The total length of the longer side, which covers both pastures, is \(50 \frac{5}{8}\) yards. - The length of the shorter side of each pasture is \(30 \frac{2}{9}\) yards. - There is no divider fence between the two pastures along the shorter side. **Solution Approach:** 1. Calculate the total amount of fencing needed. 2. Multiply the total length of fencing by the cost per yard to find the total cost. **Calculations:** - Total length of fencing includes the perimeter of the two rectangles minus the shared side. - Perimeter Calculation: - Total Length: \(50 \frac{5}{8}\) yards - Total Width: \(30 \frac{2}{9} \times 2\) (since there are two sections with the same width) - Total fencing needed = \(2 \times 50 \frac{5}{8} + 2 \times (30 \frac{2}{9}) - (30 \frac{2}{9})\). - Find the total cost by multiplying the total fencing length by $25.80. This problem involves calculating the perimeter of the fence required to enclose the described pastures and then determining the total cost using the given rate per yard.
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