The sum of three numbers is 123. the second number is 9 less than two times the first number. the third number is 6 more than three times the first number. find the three number

Let the first number be x. The second number is 2x-9, and the third number is 3x+6.

x + 2x-9 + 3x+6 = 123

Collect like terms:

6x - 3 = 123

Solve:

6x = 126

x = 21

Plug the x-value back in:

(2 x 21) - 9 = 33

(3 x 21) + 6 = 69

The three numbers are 21, 33, and 69.