Question

4 points
a) Find three consecutive even 24
number whose sum is 240 find
numbers​

Answer 1

Question :-

Find the three consecutive even numbers whose sum is 240.

Answer :-

• The three consecutive even numbers whose sum is 240 are 78, 80 and 82.

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To find :-

Three consecutive even numbers whose sum is 240.

Step-by-step explanation :-

The numbers are even and they are also consecutive.

It is given, that their sum is 240.

Now, let the first number be x.

Then the other two numbers will be x + 2 and x + 4 respectively.

This is because 2 and 4 are even numbers, while 1 and 3 are not, and also because these two even numbers are consecutive.

Now clearly, these numbers will add up to 240.

So, we get :-

$\sf (x) + (x + 2) + (x + 4) = 240$

Removing the brackets,

$\sf x + x + 2 + x + 4 = 240$

Adding all the variables and the constants separately,

$\sf 3x + 6 = 240$

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

$\sf 3x = 240 - 6$

On simplifying,

$\sf 3x = 234$

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

$\sf x = \dfrac{234}{3}$

Dividing 234 by 3,

$\sf x = 78.$

Since the first number (x) = 78,

Therefore, the other two numbers are as follows :-

$\Rightarrow$ x + 2 = 78 + 2 = 80.

$\Rightarrow$ x + 4 = 78 + 4 = 82.

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Verification :-

To check our answer, we just have to add these three numbers and see whether we get 240 or not.

78 + 80 + 82 = 240.

Since these three consecutive even numbers add up to 240,

Hence verified!

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Answer 2

Answer:

Question :-

Find the three consecutive even numbers whose sum is 240.

Answer :-

The three consecutive even numbers whose sum is 240 are 78, 80 and 82.

______________________________________

To find :-

Three consecutive even numbers whose sum is 240.

Step-by-step explanation :-

The numbers are even and they are also consecutive.

It is given, that their sum is 240.

Now, let the first number be x.

Then the other two numbers will be x + 2 and x + 4 respectively.

This is because 2 and 4 are even numbers, while 1 and 3 are not, and also because these two even numbers are consecutive.

Now clearly, these numbers will add up to 240.

So, we get :-

\sf (x) + (x + 2) + (x + 4) = 240(x)+(x+2)+(x+4)=240

Removing the brackets,

\sf x + x + 2 + x + 4 = 240x+x+2+x+4=240

Adding all the variables and the constants separately,

\sf 3x + 6 = 2403x+6=240

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

\sf 3x = 240 - 63x=240−6

On simplifying,

\sf 3x = 2343x=234

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

\sf x = \dfrac{234}{3}x=

3

234

Dividing 234 by 3,

\sf x = 78.x=78.

Since the first number (x) = 78,

Therefore, the other two numbers are as follows :-

\Rightarrow⇒ x + 2 = 78 + 2 = 80.

\Rightarrow⇒ x + 4 = 78 + 4 = 82.

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Verification :-

To check our answer, we just have to add these three numbers and see whether we get 240 or not.

78 + 80 + 82 = 240.

Since these three consecutive even numbers add up to 240,

Hence verified!

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