Question

the sum of three consecutive even numbers is 42 what are the numbers ​

Answer 1

Answer:

$\qquad\qquad\underline{\textsf{\textbf{ \color{pink}{Question :-} }}}$

• The sum of three consecutive even numbers is 42 what are the numbers.

$\qquad\qquad\underline{\textsf{\textbf{ \color{magenta}{Given :-} }}}$

• The sum of three consecutive even numbers is 42.

$\qquad\qquad\underline{\textsf{\textbf{ \color{green}{Find\: Out :-} }}}$

• What are the numbers.

$\qquad\qquad\underline{\textsf{\textbf{ \color{blue}{Solution :-} }}}$

Let the three even numbers be x, x+2, x+4

Now it is given that their sum is 42,

☣ According to the question :-

➙ x + x + 2 + x + 4 = 42

➙ 3x + 6 = 42

➙ 3x = 42 - 6

➙ 3x = 36

➙ x = $\sf \cancel{\dfrac{36}{3}}$

➙ ${\small{\bold{\purple{\underline{x = 12}}}}}$

Hence the first even term is 12.

The other terms are:

☢ x + 2 = 12 + 2 = $\red{ \boxed{\sf{14}}}$

☢ x + 4 = 12 + 4 = $\red{ \boxed{\sf{16}}}$

Henceforth, the consecutive terms are 12, 14 and 16.

Answer 2

Given :-

• The sum of three consecutive even numbers is 42

To Find :-

• What are the numbers?

Solution :-

Let, first number be y

And, second number be (y + 2)

Also, third number be (y + 4)

We know that,

✪ Sum of these numbers = 42 ✪

Since,

⇒ $\sf y + (y + 2) + (y + 4) = 42$

⇒ $\sf y + y + 2 + y + 4 = 42$

⇒ $\sf y + y + y + 2 + 4 = 42$

⇒ $\sf 3y + 6 = 42$

⇒ $\sf 3y = 42 - 6$

⇒ $\sf 3y = 36$

⇒ $\sf y = {\cancel{\dfrac{36}{3}}}$

➠ $\bf{\red{y = 12}}$

So required numbers are,

✧ First number = y = 12

✧ Second number = y + 2 = 12 + 2 = 14

✧ Third number = y + 4 = 12 + 4 = 16

Hence, required even numbers are 12, 14 and 16.

Let's verify :-

We know that,

✪ Sum of these numbers = 42 ✪

Since,

⇒ $\sf y + (y + 2) + (y + 4) = 42$

Put y = 12 in above equation we get,

⇒ $\sf 12 + (12 + 2) + (12 + 4) = 42$

⇒ $\sf 12 + 14 + 16 = 42$

⇒ $\sf 42 = 42$

➠ $\bf{\purple{LHS = RHS}}$

Hence, Verified ✔