Question

when you reverse the digits in a certain two digit number you increase its value by 18.what is the number if the sum of its digit is 14

Answer 1

We have a number of two digits that we call xy, we know that x+y=14 and yx-xy=18.

Due x and y could be integers between 0 and 9, we can write the following equations:

`\begin{gathered} x+y=14 \\ (y-1)-x=1 \\ \end{gathered}`

The second equation represent the condition that yx-xy=18, to satisfy that condition we assume that y borrow an unit to x so 1x-y=8, so (y-1)-x=1.

Now, we solve the equations:

`\begin{gathered} x+y=14\Rightarrow y=14-x \\ (14-x-1)-x=1 \\ 13-2x=1 \\ 2x=13-1=12 \\ x=(12)/(2)=6 \\ \text{And:} \\ y=14-6=8 \end{gathered}`

So, the number is 68, and 86-68=18.