# Whose rating is higher?

Algebra Level 4

Jim and Bob are maths students who both use Brilliant.Their rating increases by $$(\frac{P-C}{25})^{2}$$ when they solve a problem with a rating higher than their own rating,where $$C$$ is their current rating and $$P$$ is the rating of the problem they solved.When they get a problem wrong, their rating decreases by $$(\frac{P-C}{25})^{2}$$ if the rating of the problem solved wrongly is less than their current rating and their rating decreases by $$\frac{4C}{P}$$ if the rating of the problem is more than their current rating. Both of their ratings in Algebra are $$1600$$.This morning,Jim solved a problem with a rating of $$1700$$.After that,he got a problem with a rating of $$1591$$ wrong.When Bob found out that Jim's rating had increased,he immediately started doing problems on Brilliant.Bob got a problem with a rating of $$1500$$ wrong.What is the minimum rating of the next problem he has to solve correctly if he only has time to solve one problem and he wants to beat Jim or make their ratings equal?

• Assume that Brilliant ratings are rounded to the nearest integer.