Chapter 6.4, Problem 27PPE

To determine

To find: Two digit number that follows the given conditions.

Answer to Problem 27PPE

Required two digit number is 37.

Explanation of Solution

Given information: Any two digit number is calculated as $10a+b$ where a is ten`s place digit and b is ones` place digit. Also, for required number, ones`s place digit is one more than twice the tens` place digit and the value of the number is two more five times the ones` place digit.

Concept used: Form two linear equations in two variables a and b, each using giving two conditions given and then solve them for both variables. Then put the values of these variables in two digit number $10a+b$ to get required two digit numbers.

Calculation: As ones` digit is one more than twice the tens` place digit, so,

  $b=2a+1\mathrm{......}(i)$

Also, as number is two more five times the ones` place digit, so,

  $\begin{array}{l}10a+b=5b+2\\ \Rightarrow 10a-4b=2\mathrm{......}(ii)\end{array}$

By both equations,

  $\begin{array}{l}10a-4(2a+1)=2\\ \Rightarrow 10a-8a-4=2\text{using distributive rule }a(b-c)=ab-ac\\ \Rightarrow 2a=6\\ \Rightarrow a=\frac{6}{2}=3\end{array}$

By first equation,

  $b=2(3)+1=6+1=7$

So required number is,

  $10a+b=10\times 3+7=30+7=37$

Conclusion: It is obtained that required two digit number is 37.