there are 30 balls in a box; every ball is one of three colours: white, blue or red. if we take out any 25 balls from the box, there are at least 3 white balls, at least 5 blue balls and at least 7 red balls among these 25. how many balls of each color are there in the box?

Question

shubhamsrg · Answer

*

anonymous · Answer

what does * mean?

shubhamsrg · Answer

Its just a comment like any other, now I'll get a notification whenever anyone posts on this question
* just represents bookmark :|

anonymous · Answer

i tried and i got 8 white, 10 blue and 12 red but don't know if its right

shubhamsrg · Answer

can you show your work ?

shubhamsrg · Answer

because I cant figure it out

anonymous · Answer

$$20\ge w+r$$$$22\ge b+r$$$$18\ge b + w$$

anonymous · Answer

then using b+r+w=30 rearraing b to be subject and sub into inequality

shubhamsrg · Answer

20>= w+r or 10<=w+r 
shouldn't it be the latter one ?

reemii · Answer

@mr.please is right with his inequalities

shubhamsrg · Answer

I am unable to follow, 
how 20>= w+r ?

reemii · Answer

w+r+b = 30.
the number of blue balls out of 25 randomly chosen balls is 5.
That means that there are "not too many white and red ones". You are certain that you will HAVE TO select 5 red balls at least if, in the worst case scenario, you took all white and all blue ones.

reemii · Answer

is at least 5 *

anonymous · Answer

cuz there must be at least 5 blue balls

reemii · Answer

if w+b = 21, it is possible that in some draw, you take all of them, in that case, you would only obtain 4 red balls.

shubhamsrg · Answer

its taking me a little time to grasp to this. you guys please continue while I try to understand in the meantime.

shubhamsrg · Answer

I am assuming your answer must be correct then @mr.please

anonymous · Answer

i am not sure

reemii · Answer

can you write the next steps in detail please?

anonymous · Answer

what i did next was rearrange to get r = 30 - w -b

anonymous · Answer

and sub into r <= 22-b

anonymous · Answer

this then means 30-w-b<=22-b 
--> w>=8

reemii · Answer

b >= 10 and r >= 12 with the same trick. next?

anonymous · Answer

yeah

anonymous · Answer

from there, w = 8, b= 10, r =12

anonymous · Answer

otherwise total cannot be 30

reemii · Answer

Oh I see. b+r <= 22 but at the same time, b>=10 and r>=12, which means we have 22 <= b+r <= 22. so you must choose the smallest possible r and b -> r=12, b=10. yep. well done @mr.please