Question

the sum of three consecutive even integers is 36 find the smallest of them?​

Answer 1

Answer :-

• The smallest of the three consecutive even integers is 10.

Given :-

• The sum of three consecutive even integers is 36.

To find :-

• The smallest of them.

Step-by-step explanation :-

• In this question, it has been given that the sum of three consecutive even integers is 36 and we have to find the smallest number among them. We know that even numbers are divisible by 2 and they differ by 2 as well. Let's use this knowledge to first find these numbers and then we can find the smallest one between them.

Calculations :-

• Let the first number be x.

• Then the second number will be (x + 2) and the third number will be (x + 4).

• The sum of these numbers is 36.

$\sf \implies x + (x + 2) + (x + 4) = 36$

Removing the brackets,

$\sf\implies x + x + 2 + x + 4 = 36$

Adding all the variables and constants,

$\sf \implies 3x + 6 = 36$

Transposing 6 from LHS to RHS, changing it's sign,

$\sf \implies 3x = 36 - 6$

On simplifying,

$\sf\implies 3x = 30$

Transposing 3 from LHS to RHS, changing it's sign,

$\sf \implies x = \dfrac{30}{3}$

Dividing 30 by 3,

$\sf\implies x = 10.$

• The value of x is 10.

Hence, all the numbers are as follows :-

$\rm x = 10.$

$\rm x + 2 = 10 + 2 = 12.$

$\rm x + 4 = 10 + 4 = 14.$

• The three numbers are 10, 12 and 14.

It is clear that :-

$\boxed{\bf10 \: is \: the \: smallest \: number \: here.}$

• Thus, the smallest number is 10.

Answer 2

Answer:

10

Step-by-step explanation:

In this question, it has been given that the sum of three consecutive even integers is 36 and we have to find the smallest number among them. We know that even numbers are divisible by 2 and they differ by 2 as well. Let's use this knowledge to first find these numbers and then we can find the smallest one between them.

Calculations :-