Question

In a two digit number, the unit's digit is 7 more than tens digit. Sum of the digits is 1/2 of the whole number. Find the digits and number.​

Answer 1

Basic Concept Used :-

Writing Systems of Linear Equations from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

$\large\underline{\bf{Solution-}}$

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{digit \: at \: units \: place = x} \\ &\sf{digit \: at \: tens \: place = y} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:Hence - \begin{cases} &\sf{number \: formed = 10y + x}\end{cases}\end{gathered}\end{gathered}$

According to statement

Unit digit is 7 more than the tens digit

$\bf\implies \:x = y + 7 - - - (1)$

According to statement again,

Sum of the digits is 1/2 of the whole number.

$\rm :\implies\:x + y = \dfrac{1}{2}(10y + x)$

$\rm :\longmapsto\:2x + 2y = 10y + x$

$\rm :\longmapsto\:2x - x = 10y - 2y$

$\rm :\longmapsto\:x = 8y$

$\rm :\longmapsto\:y + 7 = 8y \: \: \: \: \: \: \: \bf \{using \: (1) \}$

$\rm :\longmapsto\:8y - y = 7$

$\rm :\longmapsto\:7y = 7$

$\bf\implies \:y = 1$

On substituting the value of y = 1, in equation (1), we get

$\bf\implies \:x = 8$

$\begin{gathered}\begin{gathered}\bf\: It \: means-\begin{cases} &\sf{digit \: at \: units \: place = 8} \\ &\sf{digit \: at \: tens \: place = 1} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:Hence-\begin{cases} &\sf{number\: formed=10y + x = 10 + 8 = 18}\end{cases}\end{gathered}\end{gathered}$

Answer 2

Answer:

in here answer is 1,8,12 but there is only 12