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 the total length of the fence

The vertical lengths are two of $50\frac{5}{8}$ yards and three of $30\frac{9}{2}$ yards. First, convert the mixed - numbers to improper fractions. $50\frac{5}{8}=\frac{50\times8 + 5}{8}=\frac{400+5}{8}=\frac{405}{8}$ and $30\frac{9}{2}=\frac{30\times2+9}{2}=\frac{60 + 9}{2}=\frac{69}{2}$. The total length $L$ of the fence is $2\times\frac{405}{8}+3\times\frac{69}{2}$.
$2\times\frac{405}{8}=\frac{405}{4}$ and $3\times\frac{69}{2}=\frac{207}{2}$. Get a common denominator of 4: $\frac{207}{2}=\frac{414}{4}$. Then $L=\frac{405}{4}+\frac{414}{4}=\frac{405 + 414}{4}=\frac{819}{4}=204.75$ yards.

Step2: Calculate the total cost

The cost per yard is $\$25.80$. The total cost $C$ is the product of the length and the cost per yard. So $C = 204.75\times25.80$.
$C=204.75\times25.80=(200 + 4+0.75)\times25.80=200\times25.80+4\times25.80+0.75\times25.80$.
$200\times25.80 = 5160$, $4\times25.80=103.2$, $0.75\times25.80=\frac{3}{4}\times25.80 = 19.35$.
$C=5160+103.2 + 19.35=5282.55$.

Answer:

$5282.55$