Question

The sum of three consecutive multiples of 8 is 312 find the multiples

Answer 1

The multiples are 96 , 104 , 112

Given :

The sum of three consecutive multiples of 8 is 312

To find :

The multiples

Solution :

Step 1 of 2 :

Form the equation

Three consecutive multiples of 8 are 8x , 8x + 8 , 8x + 16

Here it is given that sum of three consecutive multiples of 8 is 312

So by the given condition

$\displaystyle \sf{ 8x + (8x + 8) + (8x + 16) = 312}$

Step 2 of 2 :

Find the multiples

$\displaystyle \sf{ 8x + (8x + 8) + (8x + 16) = 312}$

$\displaystyle \sf{ \implies 8x + 8x + 8 + 8x + 16= 312}$

$\displaystyle \sf{ \implies 24x + 24= 312}$

$\displaystyle \sf{ \implies 24x = 288}$

$\displaystyle \sf{ \implies x = \frac{288}{24} }$

$\displaystyle \sf{ \implies x = 12 }$

1st multiple = 8x = 8 × 12 = 96

2nd multiple = 8x + 8 = 96 + 8 = 104

3rd multiple = 8x + 16 = 96 + 16 = 112

Hence the multiples are 96 , 104 , 112

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Answer 2

Given,

The sum of 3 consecutive multiples of 8 = 312

To find,

The three consecutive multiples of 8.

Solution,

These three consecutive multiples of 8 will be 96, 104 and 112.

We can easily solve this problem by following the given steps.

We know that we get the two consecutive multiples of 8 by adding 8 to its previous multiple.

Let's take the first multiple of 8 to be x.

Then, the second multiple will be (x+8) and the third multiple will be (x+16).

The sum of 3 consecutive multiples of 8 = 312

x + (x+8) + (x+16) = 312

3x + 24 = 312

3x = 312 - 24 ( Moving 24 from the L.H.S. to R.H.S. will change its sign from plus to minus.)

3x = 288

x = 288/3

x = 96

So, the first multiple of 8 will be 96.

Then, the second multiple will be 104 (96+8).

The third multiple will be 112 (96+16).

Hence, the three consecutive multiples of 8 will be 96,104 and 112.