Chapter 9.7, Problem 5OE

To determine

To express: the value of the two-digit number in terms of t and u .

Answer to Problem 5OE

The value of 2-digit number is $\frac{3u}{2}$ .

Explanation of Solution

Given information:

A two-digit number has tens digit t and units digit u .

The tens digit is one half 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 ones digit of the original number.

Therefore, the tens digit will be $=\frac{1}{2}(u)$

	Tens	Units	Value
Original number	$\frac{1}{2}(u)$	$$ u	$\begin{array}{l}=\frac{1}{2}(u)+u\\ =\frac{u}{2}+u\\ =\frac{u+2u}{2}\\ =\frac{3u}{2}\end{array}$

Hence, the value of 2-digit is $\frac{3u}{2}$ .