3 numbers are in the ratio 3:5:7. if the larger number is multiplied by 3, the result is 26 more then the sum of the first and second numbers. Use an algebric solution to find the numbers

Let the largest number be 7x.

(x will have to be an integer; otherwise the three numbers cannot be integers)
The sum of the first and second numbers is then 8x.

7x * 3 = 21x = 8x + 26
13x = 26
x = 2

The three numbers are 6,10, and 14.

To solve this problem algebraically, let's assume the ratio of the three numbers is 3x:5x:7x, where x is a constant.

According to the problem, if the larger number (7x) is multiplied by 3, the result is 26 more than the sum of the first and second numbers (3x + 5x + 26). We can write this as an equation:

3 * 7x = 3x + 5x + 26

Simplifying the equation:

21x = 8x + 26

Subtracting 8x from both sides:

13x = 26

Dividing both sides by 13:

x = 2

Now that we know x = 2, we can find the three numbers:

First number: 3x = 3 * 2 = 6
Second number: 5x = 5 * 2 = 10
Third number: 7x = 7 * 2 = 14

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