Chapter 9.7, Problem 4P

To determine

To express: the equations expressing the fact.

Answer to Problem 4P

The expression is $100h+10t+u=16h+16t+16u$ .

Explanation of Solution

Given information:

A three − digit number is sixteen times the sum of its 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.

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

According to the question:-

  $\begin{array}{l}=100h+10t+u=16(h+t+u)\\ =100h+10t+u=16h+16t+16u\\ \end{array}$

Hence, the expression is $100h+10t+u=16h+16t+16u$ .