Question

Three consecutive integers are such that if taken in increasing order and multiplied by 2,3 and 4
respectively, they add upto 72. Find these numbers.​

Answer 1

Correct Statement is

• Three consecutive integers are such that if taken in increasing order and multiplied by 2,3 and 4 respectively, they add up to 74. Find these numbers.

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

Basic Concept Used :-

Writing System of Linear Equations from Word Problems

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.

Let's solve the problem now!!

$\begin{gathered}\begin{gathered}\sf \:Let \: three \: consecutive \: integers \: be \: \begin{cases} &\sf{x} \\ &\sf{x + 1}\\ &\sf{x + 2} \end{cases}\end{gathered}\end{gathered}$

According to statement,

• Three consecutive integers are such that if taken in increasing order and multiplied by 2,3 and 4 respectively, they add upto 74.

$\rm :\implies\:2x + 3(x + 1) + 4(x + 2) = 74$

$\rm :\longmapsto\:2x + 3x + 3 + 4x + 8 = 74$

$\rm :\longmapsto\:9x + 11 = 74$

$\rm :\longmapsto\:9x = 74 - 11$

$\rm :\longmapsto\:9x = 63$

$\rm :\implies\:x = \dfrac{63}{9} = 7$

$\begin{gathered}\begin{gathered}\sf Hence, \: three \: consecutive \: integers \: be \: \begin{cases} &\sf{7} \\ &\sf{8}\\ &\sf{9} \end{cases}\end{gathered}\end{gathered}$