#1**+10 **

The reciprocal of \(5\) is \(\frac{1}{5}\).

The reciprocal of a number, let's say \(x\), is \(\frac{1}{x}\).

(I'm assuming both are reciprocals because you said reciprocals.)

\(\frac{1}{5} + \frac{1}{x} = \frac{8}{11}\).

We need to put this under a common denominator, our smallest one being \(55\).

\(\frac{11}{55} + \frac{1}{x} = \frac{40}{55}\).

\(\frac{1}{x} = \frac{29}{55}\).

Cross multiplying, we get

\(29x = 55\).

\(x = 55 \div 29\).

\(x = 1.89655...\)

You can round this to any digit needed, but I'm going to round it to the hundredths, making our answer \(\boxed{1.90}\).

KnockOut Nov 13, 2018