Question

There are 4 consecutive even integers that sum to 52. What is the greatest of the 4 integers?

Answer 1

Answer:

Given,

Sum of 4 consecutive even integers = 52.

To Find :-

Value of the Greatest Integer.

Solution :-

Let ,

The four consecutive even integers be :-

• x

• x + 2

• x + 4

• x + 6

According to Question :-

x + x + 2 + x + 4 + x + 6 = 52

x + x + x + x + 2 + 4 + 6 = 52

4x + 12 = 52

4x = 52 - 12

4x = 40

x = $\sf\dfrac{40}{4}$

x = 10

$\sf\therefore$ x = 10.

$\sf\implies$ x + 2 = 10 + 2 = 12

x + 4 = 10 + 4 = 14

x + 6 = 10 + 6 = 16

$\sf\therefore$ x , x + 2 , x + 4 , x + 6 = 10 , 12 ,14 , 16.

Hence the Greatest Number = x + 6 = 16.