Chapter 3.1, Problem 11P

To determine

To calculate: The digits of a positive two-digit integer $N$ are interchanged to form an integer $K$ and all possibilities for $N$ under the conditions.

Answer to Problem 11P

So, possible conditions are $N=21,K=12$ and $N=13,K=31$ .

Explanation of Solution

Given information: The sum of $K$ and twice $N$ is less than 60.

Calculation: Let the tens digit be $x$ and the digit be $y$ then,

  $\begin{array}{l}N=10x+y\\ \text{and according to the give condition then,}\\ K=10y+x\\ \text{then the required inequality becomes,}\\ K+2N<60\\ \left(10y+x\right)+2\times \left(10x+y\right)<60\\ 10y+x+20x+2y<60\\ 21x+12y<60\mathrm{...}\left(1\right)\\ \text{Possible conditions are,}\\ \text{at }x=2,y=1\text{ putting value in equation}\left(1\right)\\ N=21,K=12\\ \text{at }x=,y=3\text{ putting value in equation}\left(1\right)\\ N=13,K=31\end{array}$

So, possible conditions are $N=21,K=12$ and $N=13,K=31$ .