Two numbers differ by 3. The sum of their reciprocals is seven tenths. How do you find the numbers?
Tthere are two solutions to a problem:
This is a typical problem that can be solved using a system of two equations with two unknown variables.
Let the first unknown variable be
The difference between them is
Their reciprocals are
Incidentally, existence of reciprocals necessitates the restrictions:
To solve this system, let's use the method of substitution.
From the first equation we can express
From equation (1) we can derive:
Substitute it into equation (2):
Incidentally this necessitates another restriction:
Using common denominator
This is a quadratic equation that can be rewritten as:
Two solutions to this equation are:
So, we have two solutions for
In both cases
Let's check the second condition:
(a) for a solution
(b) for a solution
Both solutions are correct.