The answer: The 3 (three) consecutive odd integers are: -3, -1, 1. _____________________________________________ Explanation: _______________ To represent 3 (three consecutive odd integers): ____________________________________ Let "x" be the first odd integer. ____________________________________ Let "(x+2)" be next consecutive odd integer. ____________________________________ Let "(x+4") be the third odd integer. ____________________________________ The sum of these three consecutive odd integers: __________________________________________ x + (x + 2) + (x + 4) = x + x + 2 + x + 4 = 3x + 6 ; _________________________________________ Six ("6") times the sum of these 3 (three) consecutive odd integers = _________________ 6*(3x+6) = 6(3x + 6) = -18 (as given in the problem). _____________________________________________ Given: 6(3x + 6) = -18 ; We can divide EACH SIDE of the equation by "6", to cancel the "6" on the left-hand side into a "1"; __________________________________________ {6(3x + 6) } / 6 = -18 / 6 ; to get: ________________________________________ 3x + 6 = -3 ; Now, we can subtract "6" from EACH SIDE of the equation: __________________________________ 3x + 6 - 6 = -3 - 6 ; to get: __________________________________ 3x = -9 ; Now, we can divide EACH SIDE of the equation by "3"; to isolate "x" on one side of the question; and solve for "x" ; ___________________________________ 3x / 3 = -9 / 3 ; x = - 3 ; _____________________ Remember, from above: __________________________ Let "x" be the first odd integer. We know that "x = -3". Is this an odd integer? Yes! ____________________________________ Let "(x+2)" be next consecutive odd integer. So (x+2) = (-3+2) = -1. Is this an odd integer? Yes! Is this "{-1}" the next consecutive odd integer with respect to "{-3}"? Yes! ____________________________________ Let "(x+4") be the third odd integer. So (x+4) = (-3+4) = 1. Is this an odd integer? Yes! Is this "{1"} the next consecutive odd integer with respect to "{-1}"? Yes! ___________________________ So, our 3 (three) consecutive odd integers are: -3, -1, 1. ___________________________ To check our work: Is 6 times the sum of our 3 consecutive odd integers, equal to "(-18)" ?
The sum of our 3 consecutive odd integers = -3 + (-1) + 1 = -3 - 1 + 1 = -3.
There are, 3 x 2 x 1 = 6 possible ways of arranging the three digits. Therefore in that set of 720 possibilities, each unique combination of three digits is represented 6 times. So there are 720 possible combinations.
