Question

Sum of three consecutive even numbers is 54. Find the numbers.​

Answer 1

$\red{\bigstar}$ The numbers are

$\large\leadsto\boxed{\rm\purple{16}}$

$\large\leadsto\boxed{\rm\purple{18}}$

$\large\leadsto\boxed{\rm\purple{20}}$

• Given:-

Sum of three consecutive even numbers is 54.

• To Find:-

The numbers

• Solution:-

Let the three consecutive even numbers be n,n+2,n+4.

• According to the question:-

→ $\sf n + (n+2) + (n+4) = 54$

→ $\sf n + n + 2 + n + 4 = 54$

→ $\sf 3n + 6 = 54$

→ $\sf 3n = 54 - 6$

→ $\sf 3n = 48$

→ $\sf n = \dfrac{48}{3}$

$\pink{\bigstar}$ $\large{\underline{\underline{\bf\green{16}}}}$

Now,

n = 16

n+2 → 16+2 = 18

n+4 → 16+4 =20

Therefore, the numbers are 16,18 and 20.

$\pink{\bigstar}$ Verification:-

→ 16 + 18 + 20

→ 34 + 20

→ 54

★ HENCE VERIFIED★

Answer 2

Let the first even number = x

second even number = x + 2

and third even number = x + 4

According to the condition,

x + x + 2 + x + 4 = 54

⇒ 3x + 6 = 54

⇒ 3x = 54 – 6

⇒ x = 48/3 = 16

∴ First even number = 16

First even number = 16Second even number = 16 + 2 = 18

First even number = 16Second even number = 16 + 2 = 18and third even number = 16 + 4 = 20