Chapter 9.7, Problem 2ST

To determine

To solve: the problems about two-digit numbers.

Answer to Problem 2ST

The number is 96.

Explanation of Solution

Given information:

The sum of the digits in a two-digit number is 15. If the digits are reversed , the number is decreased by 27.

Formula used:

Digit problems are based on our decimal system of numeration.

Step1. The problem asks for the original number.

Step2. Let t = the tens digit of the original number.

Let u = the units digit of the original number.

Step3. Use the facts of the problem to write two equations.

Step4. Solve the equations.

Calculation:

Consider ,

Let t = the tens digit of the original number.

Let u = the units digit of the original number.

	Tens	Units	Value
Original number	t	u	$10t+u$
Number reversed	u	t	$10u+t$

According to the question,

  $=t+u=15\text{ (i)}$

Also,

  $=10t+u-27=10u+t\text{ (ii)}$

  $\begin{array}{l}=10t+u-10u-t=27\\ =9t-9u=27\\ =\frac{9(t-u)}{9}=\frac{27}{9}\\ =t-u=3\text{ (iii)}\end{array}$

Adding equation (i) and (iii) we get,

  $\begin{array}{l}=2t=18\\ =t=9\end{array}$

Putting value of t in equation (i),

  $\begin{array}{l}=9+u=15\\ =u=15-9\\ =u=6\end{array}$

Thus , the 2-digit number is 96.