Question

The sum of three consecutive multiples of 7 is 777. Find the three numbers.

Answer 1

Hint: Multiples of a number are those numbers which are divisible by that. Like if x and y are any two numbers then if y is a multiple of x then the remainder should be equal to zero when x is divided from y.

Complete step-by-step solution -

As we know that some numbers are known as consecutive if they occur one after another or we can say that if those numbers satisfy a particular condition (here multiples of 7) then each number should be the next number that satisfies that condition.
So, let us assume any three numbers that are multiples of 7 and are also consecutive.
As we know that if a number is a multiple of 7 then it can also be written as 7x, where x can be any integer.
So, now let the first of the three numbers which is a multiple of 7 be 7x.
So, the second number should be (7x + 7) because (7x + 7) will be the next number after 7x which is a multiple of 7.
And the third number that will be the multiple of 7 will be (7x + 7 + 7). Because (7x + 7 + 7) will be the next number that is multiple of 7 after (7x + 7).
Now according to the question, the sum of these three numbers is equal to 777.
So, 7x + (7x + 7) + (7x + 7 + 7) = 777 (1)
7x + 7x + 7x + 21 = 777
So, subtracting 21 from both sides of the above equation. We get,
21x = 777 – 21 = 756
So, dividing both sides of the above equation by 21. We get,
x = \[\dfrac{{756}}{{21}} = 36\]
So, now putting the value of x in three numbers. We will get,
First number = 7x = 7*36 = 252
Second number = 7x + 7 = 7*36 + 7 = 252 + 7 = 259
Third number = 7x + 7 + 7 = 7*36 + 7 + 7 = 252 + 7 + 7 = 266
Hence, three consecutive multiples of 7 whose sum is equal to 777 are 252, 259 and 266.

Note: Whenever we come up with this type of problem we should note that if it is only given that the three numbers are consecutive then we should take them as x, x + 1, x + 2. But if it is given that they are consecutive multiples of 7 then these numbers should be 7x, 7x + 7, 7x + 14. We can also replace 7x with y in all three numbers because at last it will give us the same numbers.