The sum of the reciprocal of a number and the reciprocal of 5 less than the number is 7 times the reciprocal of the original number. Find the original number.

Question

This is a math problem that has been giving me trouble for over 30 minutes now. I'm not quite sure how to tackle it.

Answer 1

Assume x is the original number.

Then 1/x is the reciprocal.

Translate sentence into an equation: 1/x + 1/(x-5) = 7(1/x)

Solve: subtract the first term (1/x) from both sides to make things easier:

1/(x-5) = 7/x - 1/x

1/(x-5) = 6/x

Cross multiply and solve the rest:

x = 6(x-5)

x = 6x-30

-5x = -30

x = 6

Answer 2

Let x = the number

 

Then, 1/x + 1/(x-5) = 7/x

 

So, 1/(x-5) = 6/x

 

Cross multiply to get 6(x-5) = x

 

6x - 30 = x

 

5x = 30    So, x = 6