Rose Weaver

2023-02-22

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

Shiloh Hinton

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

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 : $n,n+2,n+4$
$⇒n+\left(n+2\right)+\left(n+4\right)=78←\phantom{\rule{1ex}{0ex}}\text{equation to be solved}$
$⇒3n+6=78$
Subtract 6 from both sides.
$3n\overline{)+6}\overline{)-6}=78-6$
$⇒3n=72$
To solve for n, divide both sides by 3
$\frac{\overline{)3}n}{\overline{)3}}=\frac{72}{3}$
$⇒n=24←\phantom{\rule{1ex}{0ex}}\text{first even number}$
$n+2=24+2=26←\phantom{\rule{1ex}{0ex}}\text{second even number}$
$n+4=24+4=28←\phantom{\rule{1ex}{0ex}}\text{third even number}$#
$\text{Check:}\phantom{\rule{1ex}{0ex}}24+26+28=78$

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