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