One number is 5 times as large as another. The sum of their reciprocals is . Find the two numbers.

Question

One number is 5 times as large as another. The sum of their reciprocals is  . Find the two numbers.

Quizplus · Accepted Answer

Let the smaller number be $x$. Then the larger number is $5x$. We are given that $	frac1x+	frac1{5x}=11ec1544_37e4_7068_8a2d_0d75ca549a04_TBX8671_11$, so $	frac{6}{5x}=11ec1544_37e4_7068_8a2d_0d75ca549a04_TBX8671_11$. Solving for $x$ we get $x=11ec1544_37e4_706a_8a2d_3b6c46e02f2d_TBX8671_11$. Therefore the two numbers are $11ec1544_37e4_706a_8a2d_3b6c46e02f2d_TBX8671_11$ and $5(11ec1544_37e4_706a_8a2d_3b6c46e02f2d_TBX8671_11)=11ec1544_37e4_706b_8a2d_1dc550203104_TBX8671_11$.

One Number Is 5 Times as Large as Another