Chapter 9.7, Problem 8P

To determine

To solve: the problems about two-digit numbers.

Answer to Problem 8P

The number is 27.

Explanation of Solution

Given information:

The sum of the digits of a two-digit is one third of the number. The units digit is 5 more than the tens digit.

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	$10t+u$

According to the question,

  $\begin{array}{l}=t+u=\frac{1}{3}(10t+u)\\ =3(t+u)=10t+u\\ =3t+3u-10t-u=0\\ =-7t+2u=0\text{ (i)}\end{array}$

Also,

Let t = the tens digit of the original number.

Therefore,

u = the ones digit will be

  $=u=5+t\text{ (ii)}$

Substituting equation (ii) in (i) we get,

  $\begin{array}{l}=-7t+2(5+t)=0\\ =-7t+10+2t=0\\ =-5t+10=0\\ =-5t=-10\\ =5t=10\\ =\frac{5t}{5}=\frac{10}{5}\\ =t=2\end{array}$

Putting value of u in equation (ii) we get,

  $\begin{array}{l}=u=5+2\\ =u=7\end{array}$

Thus , the 2-digit number is 27.