Question

The sum of the digits a two digit is 12 if the digits are reversed the new number increased by 54​

Answer 1

Look at the way our counting system works:

From right to left we have 1's, 10's, 100's, 1000's, etc..

21 = 2(10) + 1

235 = 2(100) + 3(10) + 5

and so forth....

Let the number be xy

The value of the original number is: 10x + y

If we reverse the digits to yx the value is 10y + x

We know: x + y = 12 as we are told this in the problem.

Reversing the digits increases the value by 54 so:

10y + x = 10x + y + 54

Moving all the variables to the left in the 2nd equation we have:

-10x - y + 10y + x = 54

-9x + 9y = 54

9(-x + y) = 54

-x + y = 54/9

-x + y = 6

So we have two equations with x and y:

x + y = 12

-x + y = 6 add the equations to eliminate x

----------------

2y = 18

y = 9

If y = 9 and x + y = 12 then x = 3

The original number is 39

The reversed number is 93

Answer 2

Answer:

Step-by-step explanation:

x + y = 12   (1)

yx = xy + 54  -->  10y + x = 10x + y + 54

--->   9x - 9y = -54   ---->   x - y = -6   (2)

(1) + (2)  --->   2x = 6   --->   x = 3

            --->   y = 9

xy = 39.