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Positive integers x and y have a product of 56 and 

x is less than y

Seven times the reciprocal of the smaller number plus 14 times the reciprocal of the larger integer equals 4. what is the value of x?

 Jun 10, 2019
edited by sinclairdragon428  Jun 10, 2019
edited by sinclairdragon428  Jun 10, 2019
 #1
avatar+248 
0

Positive integers x and y have a product of 56 and x

 
 Jun 10, 2019
 #2
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x * y = 56..............................(1)

7*1/x  +  14*1/y = 4...................(2)

Can you solve the 2 simultaneous equations? Try it.

 
 Jun 10, 2019
edited by Guest  Jun 10, 2019
 #3
avatar+101085 
+1

xy = 56   ⇒  y = 56/x

 

And

 

7 (1/x) +  14(1/y) = 4

 

7/x + 14/y  = 4

 

7/x + 14 / (56/x)  = 4

 

7/x + (14/56)x  = 4

 

7/x + (1/4) x  = 4          multiply through by  4x

 

28 + x^2 = 16x           rearrange as

 

x^2 - 16x + 28  = 0      factor as

 

(x - 14) ( x - 2)  = 0

 

Set each factor to 0  and solve for x   and we have that

 

x = 14     or x = 2 

 

And y =

 

56/14 = 4     or   56/2 = 28

 

So  (x,y)   = (2, 28)

 

 

cool cool cool

 
 Jun 10, 2019
 #4
avatar+248 
0

Thanks!

 
sinclairdragon428  Jun 10, 2019

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