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The length of a rectangular garden surrounded by a walkway is twice its width. If difference between the length and width of just the rectangular garden is 10 meters, what will be the width of the walkway if just the garden has width 6 meters?

Note: My translation :"The length of a rectangular garden surrounded by a walkway is twice its width." =>

Let L,W be the length and width of the garden respectively. Let x be the width of the walkway. According to the above statement L = 2x.

" If difference between the length and width of just the rectangular garden is 10 meters"

L - W = 10

also W = 6. => L-6 = 10 => L = 16 => x=8. but the explanation above is still not clear for me.

Please can some one explain how the author translated the above statements in to equation as above? Thanks, Vids

I have the same question....could someone please explain this example?

I have a problem here. it is said that: If the problem says ‘the difference of x and y’ it means ‘x – y’ is it true? isn't it means |x-y|, stated i other words, the distance between x and y?

The length of a rectangular garden surrounded by a walkway is twice its width. If difference between the length and width of just the rectangular garden is 10 meters, what will be the width of the walkway if just the garden has width 6 meters?

Note: My translation :"The length of a rectangular garden surrounded by a walkway is twice its width." =>

Let L,W be the length and width of the garden respectively. Let x be the width of the walkway. According to the above statement L = 2x.

" If difference between the length and width of just the rectangular garden is 10 meters"

L - W = 10

also W = 6. => L-6 = 10 => L = 16 => x=8. but the explanation above is still not clear for me.

Please can some one explain how the author translated the above statements in to equation as above? Thanks, Vids

I have the same question....could someone please explain this example?

I am unable to understand this problem too. Why do we assume uniform width for walkway?

I tried to understand the derivation of the first author, but failed to do so. So, I just drew a figure. Once you understand that the width of the rectangular garden includes the walkway and that "just the garden" lies within this rectangular, the question becomes simple.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Dear All Need great help Question 5 is referred . How to get this equation : L -2x = Length of just garden and W-2x = width of just garden , I can't find it in the question steam , please help , many thanks

The length of a rectangular garden surrounded by a walkway is twice its width. If difference between the length and width of just the rectangular garden is 10 meters, what will be the width of the walkway if just the garden has width 6 meters?

Note: My translation :"The length of a rectangular garden surrounded by a walkway is twice its width." =>

Let L,W be the length and width of the garden respectively. Let x be the width of the walkway. According to the above statement L = 2x.

" If difference between the length and width of just the rectangular garden is 10 meters"

L - W = 10

also W = 6. => L-6 = 10 => L = 16 => x=8. but the explanation above is still not clear for me.

Please can some one explain how the author translated the above statements in to equation as above? Thanks, Vids

I have the same question....could someone please explain this example?

I know this is old but word problems are my weakness. Can someone explain this please?

EDIT: where i am getting confused is I'm not sure why there can be a separate width for just the walkway. Because the walkway surrounds the garden, then shouldn't the walkway for just the garden be the width of garden plus walkway??

I know this is old but word problems are my weakness. Can someone explain this please?

Word problems become easier when you break it down into manageable chunks.

The length of a rectangular garden surrounded by a walkway is twice its width. If difference between the length and width of just the rectangular garden is 10 meters, what will be the width of the walkway if just the garden has width 6 meters?

Refer to the figure for the description.

L,W and x are the length, width of the garden and width of the walkway around the garden.

From "The length of a rectangular garden surrounded by a walkway is twice its width." , you get = 2*width of the garden ---> L' = 2*W' , where L' = length of garden with the walkway and W' = width of the garden with the walkway.

Thus, from above , you get L' = 2W' --> L+2x = 2*(W+2x)

From, "Difference between the length and width of just the rectangular garden is 10 meters" ---> L-W = 10

Finally, from "garden has width 6 meters" ---> W=6.

Now, you have 3 distinct equations and 3 variables --> solve for them.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

The length of a rectangular garden surrounded by a walkway is twice its width. If difference between the length and width of just the rectangular garden is 10 meters, what will be the width of the walkway if just the garden has width 6 meters?

Solution: Ok this one has more words than the previous examples, but don’t worry, lets break it down and see how simple it becomes. Key words: and (implies addition); twice (implies multiplication); difference between (implies subtraction where order is important); what (implies variable); is, will be (imply equal to)

Since this is a slightly more complicated problem, let us first define what we want.

'What will be the width of the walkway' implies that we should assign a variable for width of the walkway and find its value.

Thus, let width of the walkway be ‘x’.

Now, in order to find the width of walkway, we need to have some relation between the total length/width of the rectangular garden + walkway and the length/width of just the garden.

Notice here that if we assign a variables to the width and length of either garden+walkway or just garden, we can express every thing in terms of just these variables.

So, let length of the garden+walkway = L

And width of garden+walkway = W

Thus length of just garden = L – 2x

Width of just garden = W - 2x

Note: Remember that the walkway completely surrounds the garden. Thus its width will have to be accounted for twice in both the total length and total width.

Now let’s see what the question gives us.

‘Garden with width 6 meters’ translates to: Width of garden = 6 W – 2x = 6 Thus, if we know W we can find x.

‘Length of a rectangular garden surrounded by walkway is twice its width’ translates to: Length of garden + length of walkway = 2*(width of garden + width of walkway) L = 2*W

‘Difference between the length and width of just the rectangular garden is 10 meters’ translates to: Length of garden – width of garden = 10 (L – 2x) – (W – 2x) = 10 L – W = 10

Now, since we have two equations and two variables (L and W), we can find their values. Solving them we get: L = 20 and W = 10.

Thus, since we know the value of W, we can calculate ‘x’

10 – 2x = 6 2x = 4 x = 2

Thus, the width of the walkway is 2 meters.

Easy wasn't it?

With practice, writing out word problems in the form of equations will become second nature. How much you need to practice depends on your own individual ability. It could be 10 questions or it could be 100. But once you’re able to effortlessly translate word problems into equations, more than half your battle will already be won.

Let us now move onto specific word problem topics:

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