Chapter 9.7, Problem 6P

To determine

To express: the equations expressing the fact.

Answer to Problem 6P

The expression is $100h+10t+u=100u+10t+h-198$ .

Explanation of Solution

Given information:

When the digits of a three −digit number are reversed, the new number is 198 less than the original number.

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 reversed	u	t	h	$\begin{array}{l}=u(100)+t(10)+h(1)\\ =100u+10t+h\end{array}$

According to the question:-

  $=100h+10t+u=100u+10t+h-198$

Hence, the expression is $100h+10t+u=100u+10t+h-198$ .