Question

CHALLENGING QUESTION !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


Juliet has attempted 213 problems on Open Study and solved 210 of them correctly. Her friend Romeo has just joined Open Study, 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.

Answer 1

http://olimpiade.org/Forum/?qa=7848/brilliant-problem-solving

Check that out please.

Answer 2

There is no exact answer

Answer 3

@hartnn

Answer 4

You have the equation : 424 = n(5+n)

You just need to solve this!

Answer 5

by the way,what is the value of n ? @mathslover

Answer 6

@ehuman what is the final answer?

Answer 7

on the 415th question Romeo can take the lead.

Answer 8

so 415 is the answer

Answer 9

are you asking me or telling me?

Answer 10

asking

Answer 11

they math is there in my drawing, unless I made an error in the initial formula, the answer is correct.

Answer 12

this is wrong answer

Answer 13

@Directrix

Answer 14

ok reevaluating starting formula

Answer 15

ok

Answer 16

@Hero

Answer 17

Is it 414?

Answer 18

why?

Answer 19

Yeah it seems to be ... I am getting the value of the variable that I had put there as negative.

Answer 20

HELP ME!!

Answer 21

if you allow romeos average to start at 2/4 and juliets to start at 210/213, then in 415 100% correct answers later, romeo's average of .99760760555 will pass juliet's of .9952229299.
The answer is 415

Answer 22

just one question prior to that they both have the same average of .995215311

Answer 23

is he right? @mathslover and @Hero

Answer 24

Well, I have tried 3-4 methods, one answer among them is 415 :D

Answer 25

I have many varieties of answers :P

Answer 26

i don't know what is the answer

Answer 27

Then I will go for 415

Answer 28

tell me your varieties @mathslover

Answer 29

look at the formula in the drawing i did and point out what is in error with the starting formula, else it is indeed correct.

Answer 30

415 should be correct one.

Answer 31

414 = same ratio
415 = romeo has a better ratio

Answer 32

thank you guys ......for giving such a nice answer but i am still confused

I'll be back day after tomorrow with a confirm answer.

Again thank you guys .
@Hero , @ehuman and @mathslover


and please don't feel anything about me .
If i hurt you, i am sorry. :)

Answer 33

i'm pretty convinced that 415 is the answer

Answer 34

nobody's hurt, just confident until proven otherwise :)
@mayankdevnani

Answer 35

\[Juliet: \frac{ 210+415 }{ 213+415 } = 0.995222929\]\[Romeo: \frac{ 2+415 }{ 4+415 } = 0.995226730\]

Answer 36

plugging 414 yields the exact same answer (because we made it so)

Answer 37

These numbers assume that Julie doesn't get any of the remaining 202 problems right.

Answer 38

Which is ludicrous

Answer 39

That isn't the case for the answer I gave.

But you just made me realize that we're supposed to assume that she gets none right and that he gets them all right.

"what is the MINIMUM amt of problems they must attempt"

so 415 is not the answer. it is a smaller number

Answer 40

\[\frac{ 210 }{ 213 +x } = \frac{ 2 + x }{ 4 + x }\]

Answer 41

Actually

\[\frac{ 210 }{ 213 +x } <\frac{ 2 + x }{ 4 + x }\]

Answer 42

wow. turns out x > 18 only

Answer 43

@mayankdevnani i hope you see this ^_^

Answer 44

ohhhhh the minimum number, here I solved for the maximum number

Answer 45

Nicely done @Euler271

Answer 46

so what is the answer? @Euler271

Answer 47

x > 18