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 \(2n , 2n + 2 , 2n + 4\)
According to question,
The sum of three consecutive even integers is 108.
i.e. \(2n + 2n + 2 + 2n + 4 = 108\)
\(6n + 6 = 108\)
Subtract 6 both side,
\(6n = 102\)
Divide by 6 both side,
\(n=17\)
So, The numbers are
\(2n = 2\times 17 = 34\)
\(2n + 2 = 34 + 2 = 36\)
\(2n + 4 = 34 + 4 = 38\)
The sum of three consecutive even integers is 108 then integers are 34, 36, 38 .
The largest number among them is 38.
