Help with ratio problem

Three numbers are in the ratio 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. Use an algebraic solution to find the numbers. So what are the three numbers?

The numbers are in the ratio 3:5:7 and thus, their values must be 3x, 5x and 7x. Largest number is 7x and is multiplied by 3. The result is 26 more than the sum of 3x and 5x.
All we need to do is construct it like a mathematical equation and solve for x.
7x * 3 = 3x + 5x + 26 ==> Solve for x.
21x = 8x + 26
26 = (21 - 8)x
26 = 13x
x = 26/13
x = 2

The first number is 3x or 6.
The second number is 5x or 10.
The third number is 7x or 14.

Check:
14 * 3 = 26 + (6 + 10)
42 = 26 + 16
42 = 42

CORRECT

a : b : c

3c = 26 + a + b

a = 3/15x
b = 5/15x
c = 7/15x


3(7x/15) = 26 + 8x/15
21x/15 = 26 + 8x/15
13x/15 = 26
13x = 390
x = 30

a = (3/15)30
a = 6

b = (5/15)30
b = 10

c = (7/15)30
c = 14

6 : 10 : 14

3:5:7
A + B = 3C -26
6 + 10 = 3*14 -26

A = 6
B = 10
C = 14