Three consecutive integers are such that if taken in increasing order

1.	Three consecutive integers are such that if taken in increasing order and multiplied by 2,3 and 4respectively, they add upto 72. Find these numbers.
Answer» 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. $\rm :\implies\:2x + 3(x + 1) + 4(x + 2) = 74$ $\rm :\longmapsto\:2x + 3x + 3 + 4x + 8 = 74$ $\rm :\longmapsto\:9x + 11 = 74$ $\rm :\longmapsto\:9x = 74 - 11$ $\rm :\longmapsto\:9x = 63$ $\rm :\implies\:x = \dfrac{63}{9} = 7$ $\begin{gathered}\begin{gathered}\sf Hence, \: three \: consecutive \: integers \: be \: \begin{cases} &\sf{7} \\ &\sf{8}\\ &\sf{9} \end{cases}\end{gathered}\end{gathered}$

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

Answer»

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.

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

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

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

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

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

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

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