Chapter 9.7, Problem 7P

To determine

To solve: the problems about two-digit numbers.

Answer to Problem 7P

The number is 36.

Explanation of Solution

Given information:

A two-digit number is four times the sum of its digits. The tens digit is 3 less than the units 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,

  $\begin{array}{l}=10t+u=4(t+u)\\ =10t+u=4t+4u\\ =10t+u-4t-4u=0\\ =6t-3u=0\text{ (i)}\end{array}$

Also,

Let u = the units digit of the original number.

Therefore,

t = the tens digit will be

  $=t=u-3\text{ (ii)}$

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

  $\begin{array}{l}=6t-3u=0\\ =6(u-3)-3u=0\\ =6u-18-3u=0\\ =3u-18=0\\ =3u=18\\ =\frac{3u}{3}=\frac{18}{3}\\ =u=6\end{array}$

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

  $\begin{array}{l}=t=6-3\\ =t=3\end{array}$

Thus , the 2-digit number is 36.