The sum of three positive integers is 42. The smallest integer is five less than the middle integer. The middle integer is two less than the greatest integer. Define a variable, write an equation and solve to find the three integers.
If we define the smallest integer to be \(x\), then
\(x + (x+5) + (x+7) = 42.\)
\(3x + 12 = 42\)
The integers are x, x + 5, x + 7, or 10, 15, 17.