Mr. Smith's garden is 30 ft long and 21 ft wide and he would like to put a chain fence around it. The chain costs $5.00 a yard (3ft=1yd). He will support the chain by putting a metal post in each of the 4 corners and additional posts every 3 ft. The post cost $2.00 each. What is the total cos of the chain and posts?


(I have figured out an answer to this question, but I am perplexed about the steps used to arrive at the solution, and the underlying logic.)

Show your answer and your underlying computations, and we'll be glad to help clarify the logic.

S1: I divided 30 ft by 3 ft. This gives me 10 ft length for each side.
S2: I divided 21 ft by 3 ft. This gives me 7 ft width for each side.
Perimeter = 10+10+7+7 = 34.
Since chain cost $ 5.00... I multiplied it by 34 that makes the cost of the chain $170; Than I multiplied 34 by 2 that makes the cost of post $68.
Hence, the total cost of the chain and posts is $170 + $68 = $238.

Here is the part of the problem that has lead to my perplexity: given the first part of the problem - 30 ft by 21 ft and $5.00 a yard (1yd= 3ft), should not one first figure out the total cost of the chain from 30 ft length and 21 ft width, which I am unable to do... and then go on to work out the second half of the problem, which I am ,also, unable to find the solution for (... 4 corners and additional posts every 3 ft - $2.00 each.)...

The only reason I was able to make explicit the above steps was because I looked at the answer in the back of the book, and then proceeded to figure out how I could arrive at that solution (retrograde reasoning process).

Hence, I hope I have - at least- made the conundrum lucid.

Please enlighten me!!

For starters, you've got the correct answer; total cost = $238.

There are a number of ways one could set it up to drive toward the answer; no one way is incorrect if it arrives at the right answer (through a logical process and not by dumb luck). Drawing a simple diagram frequently helps in problems like this one, but it's an individual call.

One approach, for example:
Chain cost: Garden dimensions are 30 feet by 21 feet; hence perimeter total is 30 x 2 plus 21 x 2 = 102 feet = 34 yards total. Chain is 5 bucks a yard; thus chain cost = 5 * 34 = $170.

Post cost: Each 30-foot side has 9 posts not counting either corner post. Each 21-foot side has 6 posts not counting the corners. Thus the total quantity of posts is:
2 sides with 9 posts; 2 sides with 6 posts; 4 corner posts; tot = 34 posts.
At 2 bucks a post, that's $68 cost for the posts.

Again, that's just one approach of many. Draw a rough rectangle on paper, scribble in the dimensions, mark the corner posts, and mark off the interior posts (doesn't have to be pretty or precise). Looking at your diagram will probably suggest other ways you could write up equations to capture the situation.

But you got the answer; I'm not clear on what part of your process leaves you feeling that something's missing.

Thank you.

It seems that I was over analyzing the problem! I feel like a tongue-tied person.

Sincerely,
J

You're welcome, and don't sweat the over-analysis issue. If it makes you feel any better, think of it this way: Next time you're boarding an airplane, would you prefer to learn that the folks who put it together had over-analyzed, or under-analyzed, their engineering equations? :-)
Cheers!