Question

Sum of 3 consecutive integers is 69.Find the integer

Answer 1

The three consecutive integers are :

• The first integer = 22.
• The second integer = 23.
• The third integer = 24.

Given :

• The sum of three consecutive integers = 69.

To Find :

• The three consecutive integers.

Solution :

Let,

The first consecutive integer be x.

The second consecutive integer be x + 1.

The third consecutive integer be x + 2.

According to the question,

The sum of the three consecutive integers is 69.

⇒ (x) + (x + 1) + (x + 2) = 69 ----(1)

⇒ x + x + 1 + x + 2 = 69

⇒ x + x + x + 1 + 2 = 69

⇒ 3x + 3 = 69

⇒ 3x = 69 – 3

⇒ 3x = 66

⇒ x = 66 / 3

⇒ x = 22

So, the three consecutive integers are :

★ The first consecutive integer = x = 22.

★ The second consecutive integer = x + 1 = 22 + 1 = 23.

★ The third consecutive integer = x + 2 = 22 + 2 = 24.

Hence,

The three consecutive integers are 22, 23 and 24.

Verification :

From equation (1),

● (x) + (x + 1) + (x + 2) = 69

We have,

• The first consecutive integer (x) = 22.
• The second consecutive integer (x + 1) = 23.
• The third consecutive integer (x + 2) = 24.

Substitiute all the values ( the three consecutive integers ) in equation (1),

⇒ 22 + 23 + 24 = 69

⇒ 45 + 24 = 69

⇒ 69 = 69

Hence Verified !

_________________________

✒️ What is consecutive integers ?

Consecutive Numbers :

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

★ Some examples of consecutive integers :

• 1, 2, 3, 4, 5.

• 9, 10, 11, 12, 13.

• 102, 103, 104, 105, 106.

Answer 2

Answer:

Let the consecutive numbers be x - 1, x ,x+ 1

x-1+x+x+1=69

3x=69

x=69/3

x=23

therefore the numbers are

22,23,24

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