Rose Weaver

2023-02-22

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

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.

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

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 : $n,n+2,n+4$

$\Rightarrow n+(n+2)+(n+4)=78\leftarrow \phantom{\rule{1ex}{0ex}}\text{equation to be solved}$

$\Rightarrow 3n+6=78$

Subtract 6 from both sides.

$3n\overline{)+6}\overline{)-6}=78-6$

$\Rightarrow 3n=72$

To solve for n, divide both sides by 3

$\frac{\overline{)3}n}{\overline{)3}}=\frac{72}{3}$

$\Rightarrow n=24\leftarrow \phantom{\rule{1ex}{0ex}}\text{first even number}$

$n+2=24+2=26\leftarrow {\phantom{\rule{1ex}{0ex}}\text{second even number}}$

$n+4=24+4=28\leftarrow \phantom{\rule{1ex}{0ex}}\text{third even number}$#

$\text{Check:}\phantom{\rule{1ex}{0ex}}24+26+28=78$

The sum of three consecutive even numbers can be generalized as follows.

Let the 3 even numbers be : $n,n+2,n+4$

$\Rightarrow n+(n+2)+(n+4)=78\leftarrow \phantom{\rule{1ex}{0ex}}\text{equation to be solved}$

$\Rightarrow 3n+6=78$

Subtract 6 from both sides.

$3n\overline{)+6}\overline{)-6}=78-6$

$\Rightarrow 3n=72$

To solve for n, divide both sides by 3

$\frac{\overline{)3}n}{\overline{)3}}=\frac{72}{3}$

$\Rightarrow n=24\leftarrow \phantom{\rule{1ex}{0ex}}\text{first even number}$

$n+2=24+2=26\leftarrow {\phantom{\rule{1ex}{0ex}}\text{second even number}}$

$n+4=24+4=28\leftarrow \phantom{\rule{1ex}{0ex}}\text{third even number}$#

$\text{Check:}\phantom{\rule{1ex}{0ex}}24+26+28=78$