Question

Three consecutive integers are as such when they are taken in increasing order andmultiplied by 2, 3, and 4 respectively, they add up to 65. Find these numbers.

Answer 1

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

Given that

• Three consecutive integers are as such when they are taken in increasing order and multiplied by 2, 3, and 4 respectively, they add up to 65.

Let assume that

• First consecutive integer = x

• Second consecutive integer = x + 1

• Third consecutive integer = x + 2

So,

According to statement

$\rm :\longmapsto\:2x + 3(x + 1) + 4(x + 2) = 65$

$\rm :\longmapsto\:2x + 3x + 3 + 4x + 8 = 65$

$\rm :\longmapsto\:9x + 11 = 65$

$\rm :\longmapsto\:9x = 65 - 11$

$\rm :\longmapsto\:9x = 54$

$\bf\implies \:x = 6$

Hence,

First consecutive integer = 6

Second consecutive integer = 6 + 1 = 7

Third consecutive integer = 6 + 2 = 8

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Basic Concept Used :-

Writing System of Linear Equation 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.