Question

A two digit number is obtained by multiplying the sum of the digits by 8 .Also , it is obtained by multiplying the difference of the digits by 14 and adding 2 .Find the number
The answer is 72 but i need the steps​

Answer 1

Let the two digit number be 10x + y where x is the tens digit and y is the ones digit.

Now, according to the question.

10x + y = 8(x + y)

10x + y = 8x + 8y

10x - 8x + y - 8y = 0

2x - 7y =0 .................(1)

And,

10x + y = 14(x - y) + 2

10x + y = 14x-14y + 2

10x -14x + y + 14y = 2

-4x + 15y = 2  ................(2)

Now, multiplying the equation (1) by 2 and (2) by 7, we get

4x - 14y = 0

-4x + 15y = 2

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

         y = 2

Substitute y = 2 in (2), we get

-4x + 15y = 2

-4x + 15(2) = 2

-4x + 30 = 2

-4x = -28

x = 7

So, the required number is 72

Answer 2

Answer:

I've given the step by step process and it is correct also

hope it helped you