find the integers

Question

a positive integer is 1 less than another. If the reciprocal of the smaller and twice the reciprocal of the larger is 8/15, then find the two integers

Answer 1

Let x = larger integer

 

Then, x-1 = smaller integer

 

So, 1/(x-1) + 2/x = 8/15

 

Multiply by the LCD, 15x(x-1):  15x + 30(x-1) = 8x(x-1)

 

                                                       45x - 30 = 8x² - 8x

 

                                               8x² - 53x + 30 = 0

 

                                              (8x - 5)(x - 6) = 0

 

                                               x = 5/8(not an integer) or x = 6

 

So, x = 6 and x-1 = 5