One number is 3 times as large as another. The sum of their reciprocals is . Find the two numbers.

Question

One number is 3 times as large as another. The sum of their reciprocals is  . Find the two numbers.

Quizplus · Accepted Answer

Let x be the smaller number, then the larger number is 3x. The sum of their reciprocals is:

1/x + 1/3x = (3 + 1)/3x = 4/3x

So we have the equation:

4/3x = 11ebfe7e_345f_5806_96cc_4b7188ac7853_TBX8806_11

Multiplying both sides by 3x/11 gives us:

x = 11ebfe7e_345f_5809_96cc_5b3f9683f798_TBX8806_11

Therefore, the smaller number is approximately 3.3 and the larger number is approximately 9.9, which matches choice C.

One Number Is 3 Times as Large as Another