Three numbers are in the ratio of 3:5:7. If the largest number is multiplied by 3, the result is 26 more than the sum of the first and second numbers. Find the numbers.

let the numbers are 3x,5x,7x

given: largest no. is multiplied by 3
that is 7x * 3. And the result of this multiplication = 26+3x+5x.

so the equation is :-
7x * 3 = 26+3x+5x
=>21x=8x+26
=>13x=26
=>x=2
so, the given numbers are 6,10,14

now you can verify:-
14*3=26+6+10

16:10:24

tow number are in the ratio 3:7 and sum of the number is 810. find the largest number

To find the numbers, we can follow these steps:

Step 1: Set up the ratio
Let's assume the three numbers in the ratio are 3x, 5x, and 7x (where x is a constant).

Step 2: Express the problem as an equation
From the given information, we know that if the largest number (7x) is multiplied by 3, the result is 26 more than the sum of the first and second numbers (3x + 5x + 26).

So, the equation would be:
3 * 7x = 3x + 5x + 26

Simplifying the equation:
21x = 8x + 26

Step 3: Solve the equation
Subtract 8x from both sides to isolate the variable:
21x - 8x = 26
13x = 26

Divide both sides of the equation by 13 to solve for x:
x = 2

Step 4: Find the numbers
Now that we have the value of x, we can substitute it back into the original ratio to find the numbers:
First number = 3x = 3 * 2 = 6
Second number = 5x = 5 * 2 = 10
Third number = 7x = 7 * 2 = 14

Therefore, the three numbers are 6, 10, and 14.

The answer is 6, 10, 14