Juliet has attempted 213 problems on Brilliant and solved 210 of them correctly. Her friend Romeo has just joined Brilliant, and has attempted 4 problems and solved 2 correctly. From now on, Juliet and Romeo will attempt all the same new problems. Find the minimum number of problems they must attempt before it is possible that Romeo's ratio of correct solutions to attempted problems will be greater than Juliet's.

Question

directrix · Answer

@juliosaesar

I began helping you on this problem and was doing so when the site went down. 

I saved the first part of my work. Please read it. It is attached.

directrix · Answer

J's success ratio is [(210 + x)/(213 + x)]

R's success ratio is [(2 + x) / (4 + x)]

So, the minimum number of additional questions x each person will have to answer correctly before R's success ratio begins to exceed that of J will occur can be determined by solving this inequality for x: 

(2 + x) / (4 + x) > (210 + x)/(213 + x)

@juliosaesar   Your task is to solve for x. 

Post what you get or any questions, okay? Thanks.