Question

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

Answer 1

Hint: To start this question we will assume the three consecutive multiples of 7. And then according to the given conditions of the question we will formulate an equation and try to obtain the value of the variables.

Complete step-by-step answer:
To start this question, we will assume the three consecutive multiples of 7. Let the first one be x then the proceeding two numbers would be in a gap of 7 with x that is x + 7 similarly the third number would be x + 14.
Therefore, we have obtained the three consecutive multiples of 7 as x, x+7 and x+14.
Now we are given that the sum of these three consecutive multiples of 7 is 777.
Therefore, the sum of x, x+7 and x+14 would be equal to 777.

Their sum = x+x+7+x+14 = 777
$ \Rightarrow $ 3x+21=777
$ \Rightarrow $ 3x=777-21
$ \Rightarrow $ 3x=756
$ \Rightarrow $ x=${\dfrac{756}{3}}$
$ \Rightarrow $ x= 252
Therefore, we get the value of x as 252.
Then we proceed to calculate the value of the three consecutive multiples of 7.
They are given by,
x = 252
(x+7) = 252 + 7 = 259
(x+14) = 252 + 14 = 266.
Therefore, we obtain the numbers as 252, 259 and 266.

Note: In this question students can assume 3 different variables for multiples of 7 and that will make the solution more difficult. Always remember that the consecutive numbers assumed should have a difference in between them as 7.