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The sum of the digits of a two-digit number is 6. When the digits are reversed, the resulting number is 6 greater than 3 times the original number. Find the original number

 Jan 2, 2019
 #1
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+2

The number is = 15

The two digits are = 1 + 5 = 6

Reverse 15 and you get 51

3 x 15 + 6 = 51

 Jan 2, 2019
 #2
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A more algebraic way would be:\(3(10x+y)+6=10y+x\) . Now, we have \(30x+3y+6=10y+x\) . Solving, we get \(29x+6=7y. \) Solve it, and you should get 15.

 Jan 2, 2019
 #3
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+2

Let the digits be x and y

 

Let the original number = 10x + y

 

So

 

x + y =  6        ⇒    y =  6 - x    (1)

 

And we know that

 

3 (10x + y)  + 6   =  (10y + x)     

 

30x + 3y + 6  =  10y + x      (2)       sub   (1) into (2)

 

30x + 3( 6 - x)  + 6 = 10(6  - x) + x

 

30x + 18 - 3x + 6    = 60 - 10x + x

 

27x + 24  =   60 - 9x

 

36x =  36   

 

 x = 1

 

And y = 6 - x  =  6 - 1    =  5

 

The original number is

 

10x + y   =      10(1) + 5  =   15

 

 

 

cool cool  cool

 Jan 3, 2019

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