The fraction a+27a, where a is a positive integer, equals 0.865. What is the value of a?
Solution — click to reveal
We can rewrite 0.865 as 103865, set it equal to the fraction, and solve for a: a+27a103a(103−865)a135aa=103865⇒=865a+865⋅27⇒=865⋅27⇒=865⋅27⇒=135865⋅27=5⋅27865⋅27=5865=173.