Question

Cathy wants to fence in her 24 by 24 foot yard using chain link fencing. She does not need any fence along the house. What will the total cost of the fencing be if chain link fencing costs $120 for every 50 feet?

$172.80
$144.76
$131.69
$187.00

Answer 1

To determine the total cost of the fencing that Cathy needs, let's start with the fence perimeter that needs to be fenced.

Since her yard is 24 by 24 feet, and she does not need any fence along the house, we can assume that she needs fencing for three sides of the yard.

Two sides will be 24 feet long and one side will be 24 feet long, so we only need to calculate the total length of fencing needed:

\[
\text{Total length of fencing} = 24\, \text{feet} + 24\, \text{feet} + 24\, \text{feet} = 72\, \text{feet}
\]

Next, we need to calculate how much fencing she needs to buy. The chain link fencing costs $120 for every 50 feet.

Now, we will find out how many 50-foot sections are needed for 72 feet:

\[
\text{Number of sections} = \frac{72\, \text{feet}}{50\, \text{feet per section}} = 1.44\, \text{sections}
\]

Since Cathy cannot purchase a fraction of a section, she will need to round up to 2 sections.

Next, calculate the total cost for 2 sections:

\[
\text{Total cost} = 2 \times 120 = 240\, \text{dollars}
\]

Now, to check which option is correct, we should use the total footage needed to find the cost accurately:

\[
\text{Cost per foot} = \frac{120}{50} = 2.4\, \text{dollars per foot}
\]
\[
\text{Total cost} = 72\, \text{feet} \times 2.4 = 172.8\, \text{dollars}
\]

Thus, the total cost of the fencing will be:

\[
\text{Total cost} = 172.80\, \text{dollars}
\]

Therefore, the correct answer is:

\[
\boxed{172.80}
\]