Solve the following problem. show all steps (V. E. S. T.) The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. Find the numbers.?.

The sum of three numbers is 26."

x+y+z = 26

"the second number is twice the first"

y = 2x

"the third number is 6 more than the second"

z = 6+y

You have the system of equations

x + y + z = 26

2x - y = 0

-y + z = 6

Solve using Gauss-Jordan Elimination:

x+y+z = 26

-3y-2z = - 52

-y+z = 6

x+y+z = 26

y + (2/3) z = 52/3

-y+z = 6

x + (1/3) z = 26/3

y + (2/3) z = 52/3

(5/3) z = 70/3

x + (1/3) z = 26/3

y + (2/3) z = 52/3

z = 14

x = 4

y = 8

z = 14

We have three numbers:

first number=x

second number=2x

third number=2x+6

we can suggest this equation:

x+2x + (2x+6) = 26

x+2x+2x=26-6

5x=20

x=20/5

x=4

First number=x=4

second number=2x=2 (4) = 8

third number=2x+6=2 (4) + 6=8+6=14

Answer: the numbers are 4, 8 and 14.