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Ratio of Distinct Real Numbers

Source:

April 2, 2013
ratio

Problem Statement

Let aa and bb be distinct real numbers for which ab+a+10bb+10a=2.\dfrac ab+\dfrac{a+10b}{b+10a}=2. Find ab\dfrac ab.
<spanclass=′latex−bold′>(A)</span>0.6<spanclass=′latex−bold′>(B)</span>0.7<spanclass=′latex−bold′>(C)</span>0.8<spanclass=′latex−bold′>(D)</span>0.9<spanclass=′latex−bold′>(E)</span>1<span class='latex-bold'>(A) </span>0.6\qquad<span class='latex-bold'>(B) </span>0.7\qquad<span class='latex-bold'>(C) </span>0.8\qquad<span class='latex-bold'>(D) </span>0.9\qquad<span class='latex-bold'>(E) </span>1
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