the sum of three consecutive multiple of 7 is 777. find these multiple
first number = 7 n
second number = 7 n + 7
third number = 7 n + 14
7 n + 7 n + 7 + 7 n + 14 = 777
21 n + 21 = 777 Subtact 21 to both sides
21 n + 21 - 21 = 777 - 21
21 n = 756 Divide both sides by 21
n = 756 / 21 = 36
first number = 7 n = 7 * 36 = 252
second number = 7 n + 7 = 7 * 36 + 7 = 252 + 7 = 259
third number = 7 n + 14 = 7 * 36 + 14 = 252 + 14 = 266
252 + 259 + 266 = 777
x, x+7, x+14=777
3x+21 = 777
3x = 777-21 = 756
3x=756
x=756/3
x=253
therefore 1st no = 253+7 = 259
2nd no= 253+14 = 266 [ans]
To solve this problem, let's break it down step by step.
Let's assume the first number in the sequence of consecutive multiples of 7 is "x".
The second number would be "x + 7" since it is the next multiple of 7 after the first number.
The third number would be "x + 14" since it is the second multiple of 7 after the first number.
Now, we can set up the equation based on the information given:
x + (x + 7) + (x + 14) = 777
Simplifying the equation:
3x + 21 = 777
Next, let's isolate the variable "x" by subtracting 21 from both sides:
3x = 777 - 21
3x = 756
Now, divide both sides of the equation by 3 to solve for "x":
x = 756 / 3
x = 252
Therefore, the first number in the sequence is 252.
The second number is 252 + 7 = 259.
The third number is 252 + 14 = 266.
So, the three consecutive multiples of 7 that add up to 777 are 252, 259, and 266.