Answer:
The largest number is 38.
Step-by-step explanation:
Given : The sum of three consecutive even integers is 108.
To find : What is the largest number?
Solution :
Consecutive even integers are integers having a difference of two between them.
Let the three consecutive numbers be [tex]2n , 2n + 2 , 2n + 4[/tex]
According to question,
The sum of three consecutive even integers is 108.
i.e. [tex]2n + 2n + 2 + 2n + 4 = 108[/tex]
[tex]6n + 6 = 108[/tex]
Subtract 6 both side,
[tex]6n = 102[/tex]
Divide by 6 both side,
[tex]n=17[/tex]
So, The numbers are
[tex]2n = 2\times 17 = 34[/tex]
[tex]2n + 2 = 34 + 2 = 36[/tex]
[tex]2n + 4 = 34 + 4 = 38[/tex]
The sum of three consecutive even integers is 108 then integers are 34, 36, 38 .
The largest number among them is 38.
