Fencing Two Back YardsDate: 01/27/2001 at 20:44:46 From: Joanne Subject: Fencing backyards The problem my teacher gave me is: Sarah and JAne want to put a fence around their two rectangular back yards, with a single fence separating the yards. The dimensions of their back yards are shown in the diagram below. The price of fencing is $3.00 a foot. The price of the fence includes tax. If Sarah and Jane share the cost of the fence equally, how much money will each of them pay? 40' 40' '---------------------------------------------------------' 60' ' '60' ' 60' ' ' ' '---------------------------------------------------------' 40' 40' I don't understand what I'm supposed to do. Date: 01/29/2001 at 15:00:34 From: Doctor Keith Subject: Re: Fencing backyards Hi Joanne, Let's tackle this problem in three steps. First, we will figure out how many feet of fencing we need. Second, we will find out how much the fencing costs. Then we will find Sarah and Jane's cost. 1) How much fencing? We look at the picture and notice that the fencing goes on the lines you have drawn. We can thus add the lengths of all the lines. There are three sides with length 60 feet, and four sides with length 40 feet. From this we can set up an addition or a multiplication problem to find the total. I will leave this to you. If you have questions, write back. 2) Total cost Every foot costs $3, so if we had 10 feet of fencing it would cost 3 * 10 = 30 for a total of $30 dollars. We found out how many feet of fencing we have in part (1). Now let's calculate how much it will cost at $3 per foot. We saw in our little example that you have to multiply the feet of fencing times the cost per foot. Set up a multiplication problem to find the total cost. 3) Cost per person We know that two people (Sarah and Jane) are going to pay equal amounts for the fence. We need to divide the cost from part (2) into two equal parts. For example, we saw that 10' of fencing costs $30. If Sarah and Jane split this evenly, we can use division by 2 to get the amount paid by each: 30 / 2 = 15 so each would pay $15 for 10' of fencing. In your problem, Sarah and Jane are buying a lot more fencing. What would be the division problem for your question? This lets you see how you can solve more complicated problems by breaking them into smaller steps you can solve. If you have any more questions, or you would like to understand more about this problem, write back and I will be glad to help you. Best wishes, - Doctor Keith, The Math Forum http://mathforum.org/dr.math/ |
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