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# The length and width of a rectangular yard are 11 meters and 5 meters

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Math Expert
Joined: 02 Sep 2009
Posts: 55716
The length and width of a rectangular yard are 11 meters and 5 meters  [#permalink]

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20 Mar 2015, 07:23
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15% (low)

Question Stats:

81% (01:28) correct 19% (02:21) wrong based on 125 sessions

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The length and width of a rectangular yard are 11 meters and 5 meters respectively. If each dimension were reduced by x meters to make the ratio of length to width 8 to 3, what would be the value of x?

A. 1.4
B. 1.6
C. 1.8
D. 2.0
E. 2.2

Kudos for a correct solution.

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The length and width of a rectangular yard are 11 meters and 5 meters  [#permalink]

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20 Mar 2015, 08:19
1
L = 11 meters.
W = 5 meters.

Current ratio of L/W = 11/5. We want to subtract x from both of these values to get a new ratio of 8/3.

$$\frac{11-x}{5-x} = \frac{8}{3}$$

$$3(11-x) = 8(5-x)$$

$$33 - 3x = 40 - 8x$$

$$5x = 7$$

$$x = \frac{7}{5} = 1.4$$

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Posts: 7756
Re: The length and width of a rectangular yard are 11 meters and 5 meters  [#permalink]

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20 Mar 2015, 09:25
Bunuel wrote:
The length and width of a rectangular yard are 11 meters and 5 meters respectively. If each dimension were reduced by x meters to make the ratio of length to width 8 to 3, what would be the value of x?

A. 1.4
B. 1.6
C. 1.8
D. 2.0
E. 2.2

Kudos for a correct solution.

hi,
again a different approach is substituting values after understanding the properties of number...
1) the initial value or ratio is 11:5... if we subtract a value x from the two values ratio becomes 8:3..
2) the above point tells us that 11-x should be multiple of 8 and 5-x should be a multiple of 5....

now lets look at the choice..
A. 1.4
110-14=96 is multiple of 8 and 50-14=36, which is multiple of 3..so this is what we are looking for.. ans

lets look at other choices also
B. 1.6
110-16=94 is not a multiple of 8 and 50-16=34, not a multiple of 3..so this is not what we are looking for

C. 1.8
110-18=92 is not a multiple of 8 and 50-18=32, not a multiple of 3..so this is not what we are looking for

D. 2.0
110-20=90 is not a multiple of 8 although 50-20=30, a multiple of 3..so this is not what we are looking for

E. 2.2
110-22=88 is a multiple of 8 but 50-22=28, not a multiple of 3..so this is not what we are looking for

ans A
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Re: The length and width of a rectangular yard are 11 meters and 5 meters  [#permalink]

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20 Mar 2015, 12:00
1

11-x/5-x=8/3

which solves to x=7/5
=1.4
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The length and width of a rectangular yard are 11 meters and 5 meters  [#permalink]

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20 Mar 2015, 21:00
1
Bunuel wrote:
The length and width of a rectangular yard are 11 meters and 5 meters respectively. If each dimension were reduced by x meters to make the ratio of length to width 8 to 3, what would be the value of x?

A. 1.4
B. 1.6
C. 1.8
D. 2.0
E. 2.2

Kudos for a correct solution.

(11-x)/(5-x) = 8/3
x= 7/5
x= 1.4

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Schools: LBS '19 (WL)
GMAT 1: 690 Q48 V36
Re: The length and width of a rectangular yard are 11 meters and 5 meters  [#permalink]

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21 Mar 2015, 07:13
1
11-x/ 5-x = 8/3

33-3x= 40-8x

-3x+8x = 40-33

5x= 7

x=7/5 ------->1.4
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The length and width of a rectangular yard are 11 meters and 5 meters  [#permalink]

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23 Mar 2015, 01:29

$$\frac{11-x}{5-x} = \frac{8}{3}$$

8(x-5) = 3(x-11)

5x = 7

$$x = \frac{7}{5} = 1.4$$
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Posts: 55716
Re: The length and width of a rectangular yard are 11 meters and 5 meters  [#permalink]

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23 Mar 2015, 05:41
Bunuel wrote:
The length and width of a rectangular yard are 11 meters and 5 meters respectively. If each dimension were reduced by x meters to make the ratio of length to width 8 to 3, what would be the value of x?

A. 1.4
B. 1.6
C. 1.8
D. 2.0
E. 2.2

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

yardlengthandwidth_text.PNG [ 16.03 KiB | Viewed 4921 times ]

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Re: The length and width of a rectangular yard are 11 meters and 5 meters  [#permalink]

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26 Apr 2016, 13:27
$$\frac{11-x}{5-x}=\frac{8}{3}$$

$$3(11-x)=8(5-x)$$

$$33-3x=40-8x$$

$$5x=7$$

x=$$\frac{7}{5}$$
x=1.4
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Re: The length and width of a rectangular yard are 11 meters and 5 meters  [#permalink]

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05 Jan 2018, 00:23
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Re: The length and width of a rectangular yard are 11 meters and 5 meters   [#permalink] 05 Jan 2018, 00:23
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