The sum of 3 consecutive even numbers is 78. What is the second number in this sequence?

Rose Weaver

Rose Weaver

Answered question

2023-02-22

The sum of 3 consecutive even numbers is 78. What is the second number in this sequence?

Answer & Explanation

Shiloh Hinton

Shiloh Hinton

Beginner2023-02-23Added 9 answers

Assume that the father is x years old and that the combined ages of the two children is y years.
As per the question,
x=2y.....(1)
After 20 years,
x+20=y+20+20
⇒ x+20=y+40
⇒ x=y+20.....(2)
Equating (1) & (2),
y = 20
Substituting y = 20 in equation (1), we obtain
x = 40
Therefore, the father's age is 40 years.

Zack Dawson

Zack Dawson

Beginner2023-02-24Added 8 answers

Given that there is a 2 difference between even numbers,
The sum of three consecutive even numbers can be generalized as follows.
Let the 3 even numbers be : n , n + 2 , n + 4
n + ( n + 2 ) + ( n + 4 ) = 78 equation to be solved
3 n + 6 = 78
Subtract 6 from both sides.
3 n + 6 - 6 = 78 - 6
3 n = 72
To solve for n, divide both sides by 3
3 n 3 = 72 3
n = 24 first even number
n + 2 = 24 + 2 = 26 second even number
n + 4 = 24 + 4 = 28 third even number #
Check: 24 + 26 + 28 = 78

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