The sum of three integers is 92. the second number is three times the first number. the third number is ten less than twice the first number. find the integers.

We are to identify the three integers (let x, y and z be the three integers) given the conditions stated in the problem such as:
the sum of the three numbers is 92 =>  x+y+z = 92
the second number is three times the first number => y = 3x
the third number is ten less than twice the first number => 2x - 10 =z

Solving the equation, we have it:
x + y + z = 92
x + (3x) + (2x-10) =92
6x -10 = 92
6x = 92 +10
6x = 102
x = 17

solving for y:
y = 3x
y = 3*17
y = 51

solving for z, we have:
z = 2x -10
z = 2*17 - 10
z = 34 - 10
z = 24

The answers are:
x = 17
y = 51
z = 24