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:1) 'Work' Word Problems : http://gmatclub.com/forum/work-word-pro ... 87357.html2) 'Distance/Speed/Time' Word Problems : http://gmatclub.com/forum/distance-spee ... 87481.html[/quote]
The way the question is written is really confusing to me.
Like I would not read "length of a garden surrounded by a walkway is 2x its width" as the length of the garden and the walkway.
I would read is the length of JUST the garden and treat the walkway part as a detail that is not necessary relevant right from the start...
is this an official question or something you created as an example?