Question 1176836
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You can ignore one of the responses you have received, since it answers a different question than the one that is asked.<br>
I would advise you also to ignore most of the response from the other tutor, who takes 20-30 steps to start with four unknowns and four equations to end up with a single equation in one unknown.  That might be good exercise in algebra, but it is a huge waste of time.<br>
Take the time (you don't need much) to set up the problem using a single variable:<br>
1st number: x
2nd number: x-3  (3 less than the 1st)
3rd number: x-5  (2 less than the 2nd)
4th number: x-7  (2 less than the 3rd)<br>
Given that the product of the 1st, 3rd, and 4th is -6, we have<br>
{{{x(x-5)(x-7) = -6}}}<br>
Solving this algebraically means finding the roots of a cubic equation, which is a lengthy process.  Or you could finish solving the problem using a graphing calculator.<br>
But, assuming a solution is to be obtained without a calculator, I would solve the problem from here using logical reasoning and some simple calculations.<br>
The equation says the product of x, x-5, and x-7 is a negative number.  Simple analysis shows that the product is negative for values of x less than 0, or between 5 and 7.  Negative answers are far less likely, so we can look for an answer between 5 and 7.<br>
Then, since the product is EXACTLY -6, it is very likely that the factors x, x-5, and x-7 are all whole numbers.  So we try x=6 and find x(x-5)(x-7) = 6(1)(-1) = -6, as we wanted.<br>
ANSWERS:
1st number = x = 6
2nd number = x-3 = 3
3rd number = x-5 = 1
4th number = x-7 = -1<br>