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# helppp

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

Sep 20, 2018

#1
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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: $$\boxed{\frac{16}{35}}$$ .  Sep 20, 2018
edited by tertre  Sep 22, 2018
#2
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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 )

Sep 21, 2018
edited by ElectricPavlov  Sep 21, 2018
edited by ElectricPavlov  Sep 21, 2018
#3
+10

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

Find the reciprocal of the sum of the two numbers.

$$\begin{array}{|lrcll|} \hline (1) & x+y &=& 16 \\ (2) & xy &=& 35 \\ \\ \hline \\ \dfrac{(1)}{(2)}: & \dfrac{x+y}{xy} &=& \dfrac{16}{35} \\\\ & \dfrac{x}{xy}+\dfrac{y}{xy} &=& \dfrac{16}{35} \\\\ & \mathbf{ \dfrac{1}{y}+\dfrac{1}{x}} &\mathbf{=}& \mathbf{\dfrac{16}{35}} \\\\ \hline \end{array}$$ Sep 21, 2018