Question

The sum of three consecutive multiples of 7is 777. find these multiples

Answer 1

Let the three consecutive multiples of 7 be $7x$, $(7x+7)$ and $(7x+14)$. 
According to the question, the sum of the consecutive multiples of 7 is 777. 
Now, solve for $x$ in the equation. 
$7x + (7x+7) + (7x+14) = 777$
$7x+7x+7+7x+14 = 777$                           [Removing the brackets. ]
$7x+7x+7x+7+14 = 777$                           [Arranging the like terms together. ]
$21x+21 = 777$                                         [Adding the like terms on the left hand side. ]
$21x+21-21 = 777-21$                               [Subtracting both sides by 21. ]
$21x = 756$                                               [Simplifying. ]
$\frac{21x}{21} = \frac{756}{21}$              [Dividing both sides by 21. ]
$x = 36$                                                     [Simplifying. ]

$7x = 7(36) = 252$
$(7x+7) = [7(36)+7] = (252 + 7) = 259$
$(7x+14) = [7(36)+14] = (252 + 14) = 266$
∴ The three consecutive multiples of 7 are 252, 259 and 266. 

Very simple, of course. 

Hope this may help you. 

If you have any doubt, then you can ask me in the comments. 

Answer 2

Numbers are 252, 259, 266

Given : Sum of Three Consecutive Multiples of 7 is 777

To Find : Three Numbers

Step By Step Explanation :

The Three consecutive multiples of 7 will be $\textsf{x, x + 7}$ and $\textsf{x + 14}$. As their Sum is 777, We can write it as follows :

$\longrightarrow\textsf{x + (x + 7) + (x + 14) = 777}$

$\longrightarrow\textsf{x + x + 7 + x + 14 = 777}$

$\longrightarrow\textsf{3x + 7 + 14 = 777}$

$\longrightarrow\textsf{3x + 21 = 777}$

$\longrightarrow\textsf{3x + 21 - 21 = 777 - 21}$

$\longrightarrow\textsf{3x = 756}$

$\longrightarrow\textsf{x = 756/3}$

$\longrightarrow\textbf{x = 252}$

• Now Three Numbers are $\textsf{x, x + 7}$ and $\textsf{x + 14}$. Substitute the value of x in each and we get 252, 259, 266.

Therefore, Numbers are 252, 259, 266