Chapter 5.9, Problem 2P

To determine

Find two numbers whose sum is 25 and the sum of whose reciprocals is $\frac{1}{6}$ .

Answer to Problem 2P

10 and 15

Explanation of Solution

Given:

Sum of two numbers is 25 and sum of their reciprocal is $\frac{1}{6}$ .

Calculation:

Let the two numbers be a and b .

Their sum is 25 and sum of their reciprocal is $\frac{1}{6}$

So,

  $\begin{array}{l}\mathrm{a}+\mathrm{b}=25\text{ and }\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{b}}=\frac{1}{6}\\ \Rightarrow \frac{\mathrm{b}+\mathrm{a}}{\mathrm{a}\mathrm{b}}=\frac{1}{6}\\ \Rightarrow \frac{\mathrm{b}+\mathrm{a}}{\mathrm{a}\mathrm{b}}=\frac{1}{6}\cdot \frac{25}{25}\\ \Rightarrow \frac{\mathrm{a}+\mathrm{b}}{\mathrm{a}\mathrm{b}}=\frac{10+15}{(10)(15)}\end{array}$

So, by comparing , we have , the two numbers are 10 and 15.