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

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.

Explanation:

Answer 2

- 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.

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)((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=(138feet)/(8feet)=17.25`≈18

Then, the cost for this fencing project will be:

`Cost_A=((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=(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)((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.