# Two numbers differ by 3. The sum of their reciprocals is seven tenths. How do you find the numbers?

##### 1 Answer

Tthere are two solutions to a problem:

#### Explanation:

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

(1)

Their reciprocals are

(2)

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:

(3)

Substitute it into equation (2):

(4)

Incidentally this necessitates another restriction:

Using common denominator

This is a quadratic equation that can be rewritten as:

Two solutions to this equation are:

or

So, we have two solutions for

Correspondingly, using

In both cases

Let's check the second condition:

(a) for a solution

(b) for a solution

Both solutions are correct.