Question 324261
1 number is twice another number, if the sum of their reciprocal is 1/4 find the 2 numbers


Let the smaller number be S


Then the larger number is 2S, since one number is twice the other


Reciprocal of the smaller number, or S is {{{1/S}}}, and the reciprocal of the larger number is {{{1/(2S)}}}


Since the reciprocals sum to {{{1/4}}}, then we'll have: {{{1/S + 1/(2S) = 1/4}}}


Multiplying by LCD, 4S, we have: 4 + 2 = S. So S, or the smaller number is {{{highlight_green(6)}}}, and the larger number is {{{highlight_green(12)}}} (6*2).


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Check
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Smaller #: 6     ;   Larger #: 12


{{{1/6 + 1/12 = 1/4}}}


{{{2/12 + 1/12 = 1/4}}}


{{{3/12 = 1/4}}} (TRUE)