SOLUTION: One number is 2 more than 5 times another. Their product is 3. Find the numbers.

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Question 225110: One number is 2 more than 5 times another. Their product is 3. Find the numbers.
Answer by LtAurora(115) About Me  (Show Source):
You can put this solution on YOUR website!
The following relatiosn can be set up from the given information:
A=5B%2B2
AB=3
We can plug the first equation into the second:
%285B%2B2%29B=3
Distribute the B:
5B%5E2%2B2B=3
Move the 3 to the other side
5B%5E2%2B2B-3=0
This factors down to:
%285B-3%29%28B%2B1%29=0
Set these each equal to zero and solve:
5B-3=0, B%2B1=0
5B=3, B=-1
B=3%2F5
So, we have two possible answers, B=3%2F5, B=-1.
Plug this back into the first equation:
A=5%283%2F5%29%2B2
A=5
and
A=5%28-1%29%2B2
A=-3
Thus, the sets of equations are: A=5, B=3%2F5 AND A=-3, B=-1.