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

mathtoo
Sep 20, 2018

#1**+2 **

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: \(\boxed{\frac{16}{35}}\) .

tertre
Sep 20, 2018

#2**+2 **

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 )

ElectricPavlov
Sep 21, 2018

#3**+2 **

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

**Find the reciprocal of the sum of the two numbers.**

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

heureka
Sep 21, 2018