Algebra homework

Question

Two consecutive even whole numbers are selected. The difference between the reciprocals of the two numbers is 1/60. Determine the two numbers.

Answer 1

Let the 2 numbers be n and n + 2.

1/n - 1/(n + 2) = 1/60

Clear fractions and denominator by multiplying all terms by 60n(n + 2).

60(n + 2) - 60n = n(n + 2)

120 = n(n + 2)

Many ways to solve for n, such as converting to polynomial and solving with quadratic equation, or factoring.

I prefer inspection, since 10 X 10 is known to be 100, and you just need a bit more.

10 and 12 do the trick. Note that you can check by the fact that 1/10 = 6/60 and 1/12 = 5/60; difference is 1/60.