Question

Three neighbors plan to complete fencing projects this spring. As shown in the diagrams below, Neighbor A plans to fence in his rectangular backyard with a 6-foot tall wooden privacy fence. Neighbor B plans to construct a circular chain link fence around his pool. And, Neighbor C is putting a vinyl fence around three side of his front yard. Note: Diagrams are not drawn to scale. Intended fences are marked with a dashed line.
Wood fencing is sold in 8 foot sections for $111.50. Chain link fencing costs $9.75 per linear foot (in whole foot lengths). And, vinyl fencing can be purchased for $53.55 per linear yard (in whole yard lengths).

Which neighbor's fencing project will cost the most?
Which neighbor's fencing project will cost the least?

Answer 1

Answer:

- The neighbor's fencing project that will cost the most is: Neighbor A.

- The neighbor's fencing project that will cost the least is: Neighbor B.

Step-by-step explanation:

To calculate the amount of fence that Neighbor A has to put up, you need to add the following distances:

$Fence_A=5yards+8yards+25yards+8yards\\Fence_A=46yards$

Convert yards to feet (Remember that $1yard=3feet$:

$Fence_A=(46yards)(\frac{3feet}{1yard})=138feet$

You know that wood fencing is sold in 8 foot sections for $111.50, then, the number of sections for this fence will be:

$sections=\frac{138feet}{8feet}=17.25$≈18

Then,  the cost for this fencing project will be:

$Cost_A=\frac{(18sections)(\ 111.50)}{1section}=\ 2,007$

 To calculate the amount of fence that Neighbor B has to put up, you need to use the formula for calculate the circumference of a circle:

$C=2\pi r$

Where r is the radius.

In this case, the radius is:

$r=\frac{30feet+10feet}{2}=20feet$

Substituting, you get:

$C=Fence_B=2\pi (20feet)=125.66feet$≈126 feet

You know that the Chain link fencing costs $9.75 per linear foot, then, the cost for this fencing project will be:

$Cost_B=(126)(\ 9.75)=\ 1,228.5$

To calculate the amount of fence that Neighbor C has to put up, you need to add the following distances:

$Fence_C=16feet+58feet+16feet\\Fence_C=90feet$

Convert from feet to yards (Remember that $1yard=3feet$:

$Fence_A=(90feet)(\frac{1yard}{3feet})=30yards$

You know that the vinyl fencing can be purchased for $53.55 per linear yard , then, the cost for this fencing project will be:

$Cost_C=(30)(\ 53.55)=\ 1,606.5$

Therefore, the neighbor's fencing project that will cost the most is: Neighbor A.

The neighbor's fencing project that will cost the least is: Neighbor B.