Chapter MPS, Problem 4.9MPS

To determine

Find the two digit number.

Answer to Problem 4.9MPS

  $68$

Explanation of Solution

Given information:

The sum of the digits in a two-digit number is $14$ , the number itself is $2$ greater than $11$ times the tens digit.

Calculation:

The two digit number is of the form $10a+b$ , where $a$ is the tens digit and $b$ is the unit digit.

The sum of the two digit number is $14$ .

That is $a+b=\mathrm{14......}(1)$

  $2$ greater than $11$ times the tens digit.

  $\begin{array}{l}10a+b=11a+2\\ 10a+b-11a=11a+2-11a\\ -a+b=\mathrm{2.....}(2)\end{array}$

Now add equations $(1)and(2),$ then

  $\begin{array}{l}a+b=14\\ -a+b=2\\ -------\\ 2b=16\\ b=8\end{array}$

Substitute $b=8in(1),$ then

  $\begin{array}{l}a+b=14\\ a+8=14\\ a=14-8\\ a=6\end{array}$

Hence, the two digit number is $68$ .

The sum of the digits in $68$ is $6+8=14$

  $11$ times the tens digit is $11\times 6=66$ and the number $68is2$ greater than $66$ .