Question

the sum of three consecutive multiple of 12 is 376 find these multiples​

Answer 1

the sum of three consecutive multiple of 12 is 396

Since the numbers are consecutive multiple of 12, let the numbers be 12x, 12x+12 and 12x+24.

So, 12x + 12+12 + 12x+24 = 396

⇒ 36x + 36 = 396

⇒ 36x = 396 - 36 = 360

⇒ x = 340/36 = 10

The numbers are:

12x = 12*10 = 120

12x + 12 = 12*10 + 10 = 132

12x+24 = 12*10 + 24 = 144

The Numbers are 120, 132 and 144.

Please note that if you had taken the three consecutive numbers are 12x-12, 12x and 12x+12, it will be easier for calculation. Try using this.

And the question is wrong. it can not be 376. So i assumed it to be 396 which is a correct possibility.

Answer 2

Appropriate question:-

The sum of three consecutive multiple of 12 is 396.find these multiples.

Given:-

The numbers are multiple of 12 and their sum is 396.

To find:-

The numbers

Solution:-

We know that the numbers are multiple of 12 and thier sum is 396.

We know that the consecutive numbers are:-

Either,

x+(x+1)+(x+2)

or,

(x-1)+(x) +(x+1)

We will use the first one for this problem.

If it is multiple of 12.

12x+12(x+1)+12(x+2)

On RHS we get:-

12x+12(x+1)+12(x+2)=396

On further calculation we get:-

$\footnotesize\underline{\bf{ \longmapsto12x + 12(x + 1) + 12(x + 2) = 396}}$

$\footnotesize \underline{\bf{ \longmapsto12x + 12x + 12 + 12x + 24 = 396}}$

$\footnotesize\underline{\bf{ \longmapsto36x + 36 = 396}}$

$\footnotesize\underline{\bf{ \longmapsto36x = 360}}$

$\footnotesize\underline{\bf{ \longmapsto x = 10}}$

On putting the value of x we get:-

$\large\underline{\bf{ \implies12x = 12 \times 10 = 120}}$

$\large\underline{\bf{ \implies12(x + 1) = 12(10 + 1) = 12 \times 11 = 132}}$

$\large\underline{\bf{ \implies12(x + 2) = 12(10 + 1) = 12 \times 12 = 144}}$