Question

The Sum of three consecutive even integers is 162.Find the Integers.​

Answer 1

Let the first integer be x then the others will be x+1 and x+2

Given that,

Sum of the integers = 162

x + x+ 1 + x+2 = 162

3x+3 = 162

3x = 162 - 3

3x = 159

x = 159/3

x = 53

Therefore the three integers are 53, 54, 55

Answer 2

The three consecutive even integers are :

• The first consecutive even integer = 52.
• The second consecutive even integer = 54.
• The third consecutive even integer = 56.

Given :

• The sum of three consecutive even integers = 162.

To Find :

• The three consecutive even integers.

Solution :

Let,

The first consecutive even integer be x.

The second consecutive even integer be x + 2.

The third consecutive even integer be x + 4.

According to the question,

$: \implies \rm x + (x + 2) + (x + 4) = 162 \\ \\ : \implies \rm x + x + 2 + x + 4 = 162 \\ \\ : \implies \rm 3x + 6 = 162 \\ \\ : \implies \rm3x = 162 - 6 \\ \\ : \implies \rm3x = 156 \\ \\ : \implies \rm x = \dfrac{156}{3} \\ \\ : \implies \rm x = 52$

So, the three consecutive even integers are :

The first consecutive even integer = x = 52.

The second consecutive even integer = x + 2 = 52 + 2 = 54.

The third consecutive even integer = x + 4 = 52 + 4 = 56.

Hence,

The three consecutive even integers are 52, 54 and 56.

Additional Information :

Even Numbers - All the numbers which is ending with 0, 2, 4, 6 and 8, and also the numbers which is divisible by 2 are even numbers.

★ Examples :

• 12,
• 88,
• 96.

Consecutive Numbers - The numbers which follow each other from smallest to largest numbers (Ascending order) without any gap (without any missing number).

★ Examples :

• 1, 2, 3, 4, 5.
• 9, 10, 11, 12, 13.
• 102, 103, 104, 105, 106.

Consecutive Even Numbers - The numbers which follows each other from smallest to largest number (Ascending order) with a gap of 1 number and also all the numbers are divisible by 2.

★ Examples :

• 22, 24, 26, 28, 30.
• 112, 114, 116, 118, 120.
• 222, 224, 226, 228, 230.