Chapter 9.7, Problem 8OE

To determine

To express: the equations with three-digit number.

Answer to Problem 8OE

The value of 3-digit number is $u-h=1$ .

Explanation of Solution

Given information:

A three-digit number has hundreds digit h , tens digit t ,and units digit u .

The number obtained by reversing the order of the digits exceeds the original number by 99.

Formula used:

Digit problems are based on our decimal system of numeration.

Step1. The problem asks for the original number.

Step2. Let h = the hundreds digit of the original number.

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 h = the hundreds digit of the original number.

Let t = the tens digit of the original number.

Let u = the ones digit of the original number.

	Hundreds	Tens	Units	Value
Original number	$h$	$t$	$u$	$\begin{array}{l}=h(100)+t(10)+u(1)\\ =100h+10t+u\end{array}$
Number with digit reversed	u	t	h	$\begin{array}{l}=u(100)+t(10)+1(h)\\ =100u+10t+h\end{array}$

Now,

  $\begin{array}{l}\text{Original Number}=100h+10t+u\\ \text{Reversing Number}=99+\text{Original Number}\\ =100u+10t+h=99+(100h+10h+u)\\ =100u+10t+h=99+100h+10t+u\\ =100u+10t+h-100h-10t-u=99\\ =99u-99h=99\\ =u-h=1\end{array}$

Hence, the value of 3-digit is $u-h=1$ .