Expert: Josh - 9/4/2009

Question
PLEASE HELP!

I am in grade 9 and am having trouble finding the answer to this problem ...

Mason wants to put a picket fence around the total perimeter of his boundary. Each picket is 80mm wide and he needs to leave a gap of 20mm between pickets. Work out the perimeter of his section. Then calculate how many pickets he needs to complete his fence. Then calculate how much it will cost him to buy all the pickets at a price of $5.20 per picket.

...

So far I've only managed to solve the perimeter of Masons boundary which equals 141m. If anyone knows the answer or how to solve this problem please let me know, I'm desperate!  

Answer
Hi Sarah,

To understand this problem, let us draw a diagram.

Since you have already worked out the perimeter, it doesn't matter what shape it is. Any closed enclosure will do. For illustration purpose, let's say the boundary is rectangular.

A--- --- ---B
|
|
|

|
|
|
C--- --- ---D

As we unfold the boundary and sketch it on a straight line, it looks something like this:

A--- --- ---B--- ---D--- --- ---C--- ---A

In this diagram, you should see 10 pickets (each picket is represented by --- and is 80 mm wide). There are 10 gaps^ in total (each 20mm wide). In general, if there are N pickets, there will be N gaps for a closed enclosure.

Note: ^ counting each space ' ', B, C, D as a gap and A once.

So, the total perimeter P = N*w + N*g, where w and g denote the width of picket and the gap, respectively. Using w=80, g=20, with the known value P=141,000, you proceed to solve the equation 141000=80N+20N for N. The rest is just algebra. [Note: the perimeter is 141 meter in length, 1 meter equals 1000 millimeter. All measurements in the equation are expressed in mm.]

The final cost is simply N*c, where N=number of pickets, c=cost of each picket.

Good luck!