Question

problem solving fencing costs $25.80 per yard. how much does it cost to enclose two adjacent rectangular pastures as shown? the cost is $ justify your answer.

Explanation:

Step1: Calculate total length of fencing

We have 3 lengths of $50\frac{5}{8}$ yards and 4 widths of $30\frac{2}{9}$ yards. First, convert the mixed - numbers to improper fractions. $50\frac{5}{8}=\frac{50\times8 + 5}{8}=\frac{405}{8}$ and $30\frac{2}{9}=\frac{30\times9+2}{9}=\frac{272}{9}$.
The total length of the lengths is $3\times\frac{405}{8}=\frac{1215}{8}$ yards.
The total length of the widths is $4\times\frac{272}{9}=\frac{1088}{9}$ yards.
The total length of the fencing $L$ is $\frac{1215}{8}+\frac{1088}{9}$.
Find a common denominator, which is $8\times9 = 72$.
$\frac{1215}{8}\times\frac{9}{9}=\frac{10935}{72}$ and $\frac{1088}{9}\times\frac{8}{8}=\frac{8704}{72}$.
$L=\frac{10935 + 8704}{72}=\frac{19639}{72}\approx272.76$ yards.

Step2: Calculate the cost

The cost per yard is $25.80$.
The total cost $C$ is $C = 25.80\times L$.
$C=25.8\times\frac{19639}{72}$.
$25.8=\frac{258}{10}$, so $C=\frac{258}{10}\times\frac{19639}{72}$.
$C=\frac{258\times19639}{10\times72}=\frac{5067862}{720}\approx6983.14$.

Answer:

$6983.14$