Chapter 9.7, Problem 7OE

To determine

To express: the equations with three-digit number.

Answer to Problem 7OE

The value of 3-digit number is $100h+30t+31u$ .

Explanation of Solution

Given information:

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

The tens digit is three times the sum of the other two digits.

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.

Also,

  $\begin{array}{l}=t=3(h+u)\\ =t=3h+3u\end{array}$

	Hundreds	Tens	Units	Value
Original number	$h$	$t=3h+3u$	$u$	$\begin{array}{l}=h(100)+t(10)+u(1)\\ =100h+10\left(3h+3u\right)+u\\ =100h+30h+30u+u\\ =100h+30h+31u\end{array}$

Hence, the value of 3-digit is $100h+30t+31u$ .