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x^2-y^2 = 28 and x - y = 8 then what is the average of x and y?

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Sajjad1994
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x^2-y^2 = 28 and x - y = 8 then what is the average of x and y? [#permalink] New post   11 Dec 2019, 10:58
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If \(x^2-y^2 = 28\) and \(x - y = 8\) then what is the average of \(x\) and \(y\)?

A. 3.5

B. 1.75

C. 7

D. 8

E. 5
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rajatchopra1994
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Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y? [#permalink] New post   11 Dec 2019, 11:04
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SajjadAhmad wrote:
\(x^2-y^2 = 28\) and \(x - y = 8\) then what is the average of \(x\) and \(y\)?

A. 3.5

B. 1.75

C. 7

D. 8

E. 5


Explanation:
Given: x-y=8
x^2-y^2 = 28
(x+y)(x-y)=28
Putting value of x-y =8
x+y=28/8
x+y=3.5----1

As we know averge of x&y = (x+y)/2
from 1,
3.5/2= 1.75

IMO-B

:please Please Give Kudos, If you find my explanation Good Enough :please
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Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y? [#permalink] New post   11 Dec 2019, 13:09
The answer can be 7 here
7/2/2/1 = 7/2*2/1 = 7

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Poju4real
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Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y? [#permalink] New post   11 Dec 2019, 13:50
X^2 - y^2 = 28
(x+y)(x-y) = 28
(x+y)×8 = 28
(x+y) = 28/8
(x+y)/2 = 28/16
(x+y)/2 = 1.75

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Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y? [#permalink] New post   11 Dec 2019, 14:02
SajjadAhmad wrote:
If \(x^2-y^2 = 28\) and \(x - y = 8\) then what is the average of \(x\) and \(y\)?

A. 3.5

B. 1.75

C. 7

D. 8

E. 5


from the information we know that:
x^2 - y^2 = 28;
x - y = 8; and
x^2 - y^2 is a simplified form of (x+y)(x-y); thus

(x+y)(x-y) = 28
(x+y)(8) = 28
(x+y) = 28/8

since we are asked the average of x and y or (x+y)/2, thus
(28/8) / 2 = 1.75 (B)
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Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y? [#permalink] New post   11 Dec 2019, 20:13
bhvya324 wrote:
The answer can be 7 here
7/2/2/1 = 7/2*2/1 = 7

Posted from my mobile device


Dear bhvya324 ,

How u have solved to get 7 as the answer. Please explain. So we can find the mistake.
Please read Other Explained answers. Hope u will find the mistake.

Regards,
Rajat Chopra
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bhvya324
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Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y? [#permalink] New post   12 Dec 2019, 01:09
Sure,

(X+y) 8 = 28 = 28/8 = 7/2

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rajatchopra1994
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x^2-y^2 = 28 and x - y = 8 then what is the average of x and y? [#permalink] New post   12 Dec 2019, 01:21
bhvya324 wrote:
Sure,

(X+y) 8 = 28 = 28/8 = 7/2

Posted from my mobile device


bhvya324
Till Above You are right.
After this Question has asked for Average of x+y.
So we need to divide it by 2.

So, u got the value of x+y = 7/2
For Average, divide it by 2.
Therefore, 7/4 =1.75

I hope U will understand it. Pls do PM, if you didn't get it.

Regards,
Rajat Chopra
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Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y? [#permalink] New post   12 Dec 2019, 19:48
Expert Reply
SajjadAhmad wrote:
If \(x^2-y^2 = 28\) and \(x - y = 8\) then what is the average of \(x\) and \(y\)?

A. 3.5

B. 1.75

C. 7

D. 8

E. 5


Using the difference of squares, the first equation becomes:

(x + y)(x - y) = 28

Substituting, we have:

(x + y) * 8 = 28

x + y = 28/8 = 7/2 = 3.5

Thus, the average of x and y is (x + y)/2 = 3.5/2 = 1.75.

Answer: B
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Re: x^2-y^2 = 28 and x - y = 8 then what is the average of x and y? [#permalink]
12 Dec 2019, 19:48
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