Question

If the sum of three consecutive even numbers is 42, what is the middile number

Answer 1

let the 3no. be
x
x+2
x+4
so,
x+x+2+x+4=42
3x+6=42
3x=42-6=36
x=12
so x+2=12+2=14

Answer 2

Answer:

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 ✔