Question

sum of three consecutive even number is 68 more than the average of the numbers .find the middle number?

Answer 1

The middle number = 34

Given :

The sum of three consecutive even number is 68 more than the average of the numbers

To find :

The middle number

Solution :

Step 1 of 2 :

Form the equation to find the middle number

Let three consecutive even numbers are x , x + 2 , x + 4

By the given condition

$\displaystyle \sf x + (x + 2) + (x + 4) = \frac{x + (x + 2) + (x + 4)}{3} + 68$

Step 2 of 2 :

Calculate the middle number

$\displaystyle \sf x + (x + 2) + (x + 4) = \frac{x + (x + 2) + (x + 4)}{3} + 68$

$\displaystyle \sf{ \implies }3x + 6 = \frac{3x + 6}{3} + 68$

$\displaystyle \sf{ \implies }3x + 6 = \frac{3(x + 2)}{3} + 68$

$\displaystyle \sf{ \implies }3x + 6 = x + 2 + 68$

$\displaystyle \sf{ \implies }3x - x = 68 + 2 - 6$

$\displaystyle \sf{ \implies }2x = 64$

$\displaystyle \sf{ \implies }x = 32$

First number = x = 32

Second number = x + 2 = 32 + 2 = 34

Third number = x + 4 = 32 + 4 = 36

Hence middle number = 34

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