SOLUTION: The difference of the reciprocals of two numbers is 11⁄6. If large number is divided by smaller, the result is 1⅞ . Find the numbers.

You can put this solution on YOUR website!
Let's call our two numbers x and y, with x being the larger number. Their reciprocals would be 1/x and 1/y, respectively.
"The difference of the reciprocals of two numbers is 11/6": Since the difference is postive, then the larger number must come first. Since x is larger than y, its reciprocal is smaller that the reciprocal of y! So the equation is:
(Reworded) "the larger number divided by the smaller is 1 and 7/8" translates to:


We now have a system of two equations in two variables. We should be able to solve this. As usual there are several ways. Here is one:
Rewrite the second equation with an improper fraction:

This is a proportion (one fraction equals another). Cross multiply:

Divide by 8"

So the reciprocal of x is:

Substituting this into the first equation:

Multiply both sides by the Lowest Common Denominator (LCD) of all three fractions:

Simplifying:


Divide by 55:

Substituting this for y into :

So the two numbers are: 21/44 and 14/55.