helppp

The reciprocal of the sum of the two numbers can be written as $\frac{1}{x}+\frac{1}{y}$

We have $x+y=16,$ and $xy=35$ , so we can find the LCM of $x$ and $y$ .

So, we have: $\frac{x}{xy}+\frac{y}{xy}$ . Adding both fractions, we get,$\frac{x+y}{xy}$ and plugging in the values we finally attain: $\boxed{\frac{16}{35}}$ .

Your question states the sum of the numbers is 16....the reciprocal of this sum is 1/16

Did you mean to ask for the SUM of the RECIPROCALS of these numbers? (As Tertre calculated?{though Tertre used 13 instead of 16} )      ( I think the answer will be 16/35......tertre must have used '16' in calculations )

The sum of two numbers is 16 and their product is 35.

Find the reciprocal of the sum of the two numbers.

$\begin{array}{|lrcll|} \hline (1) & x+y &=& 16 \\ (2) & xy &=& 35 \\ \\ \hline \\ \dfrac{(1)}{(2)}: & \dfrac{x+y}{xy} &=& \dfrac{16}{35} \\\\ & \dfrac{x}{xy}+\dfrac{y}{xy} &=& \dfrac{16}{35} \\\\ & \mathbf{ \dfrac{1}{y}+\dfrac{1}{x}} &\mathbf{=}& \mathbf{\dfrac{16}{35}} \\\\ \hline \end{array}$