Question

•rm thinking of an integer. Half of this
integer is 3 more than one third of the next
integer. What is the integer?"

Answer 1

Given Question :-

• I am thinking of an integer. Half of this integer is 3 more than one third of the next integer. What is the integer?

Answer

Basic Concept :-

• How to write a Linear Equation from Word Problems

Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

Translate the problem to an equation.

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

• Clearly state what the variable represents.

Carry out the plan and solve the problem.

Let's do it now!!

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

$\begin{gathered}\begin{gathered}\bf \: Let - \begin{cases} &\sf{integer \: be \: x} \\ &\sf{next \: integer \: = \: x + 1} \end{cases}\end{gathered}\end{gathered}$

$\large \underline{\tt \:{ According  \: to  \: statement }}$

• Half of the integer is 3 more than one third of the next integer.

So,

$\rm :\longmapsto\:\dfrac{x}{2} = \dfrac{x + 1}{3} + 3$

$\rm :\longmapsto\:\dfrac{x}{2} - \dfrac{x + 1}{3} = 3$

$\rm :\longmapsto\:\dfrac{3x - 2(x + 1)}{6} = 3$

$\rm :\longmapsto\:3x - 2x - 2 = 18$

$\rm :\longmapsto\:x = 18 + 2$

$\bf\implies \:x = 20$

$\boxed{ \bf \: Hence \: the \: required \: integer \: is \: 20}$

Verification :-

Step : 1

• I am thinking of the integer 20

Step : 2

• Half of this integer 20 is 10

Step : 3

• 3 more than one third of next integer

• = 3 + 1/3 × 21

• = 3 + 7

• = 10

Hence, Verified