## Here's The Problem…

**Two sandboxes each contain the same amount of sand, but one is filled with black sand and other is filled with white sand. Alex scoops a full bucket of the black sand and pours it into the white sand. Alex stirs this mixture for hours (no homework, I guess) until the black and white sand are perfectly mixed. Alex then scoops a full bucket of the mixed sand and pours it into the black sand so that both sandboxes once again have the same amount of sand. Which is greater, the amount of black sand added to the white sand or the amount of white sand added to the black sand, or are they equal? — Mr. Simmons**

## Your Thoughts…

sup!

first one here

ok, after analyzing the equation, i have come up wit the following-

-there is a scoop of black in a bucket of white- black is less than white (btw this is rohan)NINJA! BLACK/WHITE->THE BLACK BUCKET

in my opinion, this problem is very interesting

-**Rohan K**

I believe that the amount of black sand added to the white was greater because when he scooped sand from the bucket with white there was stlill a little black in it. This is the Brad S. report. :)

P.S: This is fun!

What is your answer? you didn't specify.

Brad S.

For the problem, im not sure if i read it properly, but i think the answer is **pouring black into white** **<—rohan got this**, because the black is pure black when u do so, but when u pour white in to black, there r some black particles in the white, thus, my answer.

-**rohan k** ^{rohan}_{rohan}

p.s. im not sure if i read the problem correctly

That's what I got as an answer ,and honestly, this wasn't that tricky for me. I feel that my answer is the correct answer because that's also what you got. Good job, Rohan. This is the Brad S. report. :)

P.S: I'm sure you read it right.

I got that there is more black sand added to the white sand than white sand added to the black sand because like rohan said before, there is some black in the bucket of white sand, therefor it is less.

- Elliott M.

Still, u guys might think i'm right, but the solution i came up with is too simple, so i would be aware that i might be wrong

-**rohan k**

Lolz…i am genius…

I just thought of a weird way to prove our answer. Assume that both boxes contain 200 grains of sand. The bucket can hold 100 grains of sand, making the black sandbox have 100 and the white have 300. The mixture is 1/3 black sand. For the white sand to be greater than the black sand it has to be greater than 100(the amt in the black box) but that cannot be because the bucket holds only 100 grains. There cannot be equal amt because there are also some black grains in the white sandbox. In conclusion, my answer is there are more black grains than white. Does this make sense? Does anyone agree with this method?

And this works with any substitution of numbers…This ain't a coincidence

^{Madhula}_{Madhula} Madhula ^{Madhula} _{Madhula}

i hav no idea wat u just said.Well, i would say the amount of black sand added was greater because the bucket was only black sand and nothing else. The other bucket of sand that was added to the black sand had mostly white sand, but had some black sand mixed into it, so it isnt 100% one color, like the other bucket.

- **rohan k**

Well i think that if the black sand was stirred into the white, then poured back into the black sand won't the black sand have more because some of the black sand had gone back to the black sand box along with some of the white sand… i don't i could be wrong… Henry C

If you guys want you can think of it like this. you have 4 cups of chocolate milk and 4 cups of regular white milk. you take one scoop (1 cup) of chocolate milk and add it to the white milk. You stir it until the chocolate milk is mixed in as much as it can be. now you take another same size scoop of the 4/5 cup white milk 1/5 cup chocolate milk cup and you add it to the cup wsith chocolate. Since the scoop from the chocolate milk contained only 1 cup chocolate when the scoop you took from the cup of originally just white milk contained 1/5 chocolate milk and 4/5 white milk. this proves that the amount of chocolate milk added to the white milk was more of an amount added than the amount of white milk added to the chocolate milk.

This is the Brad S. report. :)

Hey guys, this is Sathvika. I think all of the thoughts and input going on is pretty good so far. However, even though all of you think the black sand will have more, have you considered it might be equal?

Take the initial bucket of mixed sand: Half a bucket of black sand and half a bucket of white sand goes into that one mixed sand bucket: I think they would be equal because:

a) the bucket is supposedly comprised of 50% black sand and 50% white sand (to be perfectly mixed)

b) 50% of the mixed sand goes to the black box and 50% of the mixed sand goes to the white box.

c) if it was perfectly mixed, then 25% black and 25% white would go into the black box.

d) 25% black and 25% white would go into the white box.

Thus making it equal.

I'm not sure if I'm right, but that's my thoughts on the problem. Tell me what you think.

-Sathvika R.

It could be right Sathvika…but the problem is that we have to assume 2 variables…the amt in the sandbox…and the amt the bucket can hold.

If the bucket could hold as much as the sandbox…then what you say would be equal but if you do it my way then there will be more black sand added to the white.

The real problem here is figuring out the value of atleast one vriable…if you substitute assuming random numbers you could end up with both our answer choices (THERE IS DEFINATELY NOT MORE WHITE SAND THAN BLACK ADDED!)…therefore, I am utterly confused and torn between two.

^{Madhula}_{Madhula} Madhula ^{Madhula} _{Madhula}

I'm second guessing my previous response because I may have not read the question right.

So let's break the problem down:

a) 2 sandboxes. 1- black sand 1- white sand

b) 1 bucket of black sand is poured into white sand box —> black sandbox has less sand than white sandbox

c) white sandbox is stirred into a perfect mixture = 50% black sand and 50% white sand. **HOWEVER it can't be a perfect 50/50 mixture in the white sandbox because 1 bucket of black sand is less than a whole sandbox of white sand.**

d) alex scoops a bucket of mixed sand and puts it back into the black sand to make each sandbox equal.

**HOWEVER the problem doesn't specify if he used the SAME BUCKET he scooped the black sand with or if he used a NEW BUCKET.**

**IF**

*he used a new bucket:* then wouldn't it be equal?

*he used the bucket with the black sand:* then the black sand would obviously be more because there were still black particles in the original bucket which combined into the "perfect mixture"

So I don't think the problem gave you enough information. Or I just totally over-analyzed it. :)

-Sathvika R.

You did…no matter what bucket he uses the amount being transfered will not change. If the buckets are different sizes, then the problem should specify…otherwise it isn't even a problem.

Another thing is that when the full bucket of black sand was transfered into the white sand the black sand was 100%black…but when it is transfered back the blsck sand is partiallly mixed with some white sand. Though the white sand is the majority in the bucket, it is not 100% pure white. Which comes to prove that no matter how much black sand was poured into the white sand, when "perfectly mixed"(an equal ratio of b:w), then transfered back, there is bound to be *some* black sand in the white bucket(making it less than 100%). In conclusion i keep my same last answer…more black sand was added to the white sand than white sand added to the black sand.

In the end:you end up with:

B +amt black sand and amt of whit sand (in a b:w ratio) = W +1 bucket of pure black

^{Madhula}_{Madhula} Madhula ^{Madhula} _{Madhula}

After analyzing this problem over and over again, I've concluded that if Alex (the names are different in all the periods o.o) used the same bucket to scoop the black sand over to the white and the black/white mixture back into the black sandbox, the amount of black sand will always be greater than the amount of white sand the mixture has.

Also noting, Alex would not be able to use the full potential of a larger bucket because as the problem stated: Alex then scoops a full bucket of the mixed sand and pours it into the black sand so that **both sandboxes once again have the same amount of sand**.

In analysis the amount of black sand will always be greater than the white sand because there is always simply more black sand in the sandbox added with the black sand in the bucket to overcome the amount of white sand in the bucket.

He cannot use a larger bucket because it would be ineffective as he has to have the same amount of sand in both buckets.

**Edit:** I thought that when Sathvika said new bucket and same bucket she meant that the buckets were different sizes.

—**John Y.**

Wait, John, where'd the larger bucket idea come from in the first place? Haha.

-Sathvika R.

Guys, the answer might be that it's equal. When Alex moves one full bucket of black sand into the white sand, the bucket is 100% black sand. Then, the black is mixed with the white sand, and one bucket of the mixture goes back to the box of black sand. Since it's a mixture, some of the black sand goes back to it's own box of black sand. Let's put it into numbers:

Say there is 10 buckets of sand in each sandbox.

10 buckets of white sand 10 buckets of black sand

+1 bucket of black sand -1 bucket of black sand

10 buckets of white, 1 bucket of black (11 total) 9 buckets of black sand (9 total)

-1 mixed bucket: -10/11 bucket of white, -1/11 bucket of black +1 mixed bucket: +10/11 bucket of white, +1/11 of black

9 and 1/11 bucket of white, 10/11 bucket of black 9 and 1/11 bucket of black, 10/11 of white

That shows (in numbers) why the answer is that there is 10/11 bucket of white added to the black sandbox and 10/11 bucket of black added to the white sandbox. When you scoop the mixture back into the black, you are bringing back a little bit of black back into the black sandbox.

So, that's my thoughts. I might be wrong, but I'm pretty sure that I'm right. If I'm wrong, yall can all "own" me in class tomorrow. If I'm right, I'm right. But, after deep analysis, my conclusion is that there is an equal amount added in both.

-**Jonathan Y.**

Ohh. I seem to have read the problem wrong. I thought it was asking if the amount of white sand added to the black sand was greater than the amount of the black sand already in it. I'm agreeing with Jonathan.

The other easier way to think of it is that the bucket is as large as the sandbox.

The entire sandbox of black sand would be dumped into the white one by the bucket. Then mix… And then we move half of the "perfect mixture" back into the empty sandbox, meaning that now we now have a 1:1 ratio of black and white sand in each box.

—**John Y.**

John, thanks for agreeing with me, but the bucket can't be as large as the sandbox. The problem states that "Alex then scoops a full bucket of the mixed sand and pours it into **the black sand**. Notice it **doesn't** say "Alex pours the mixture back into the **sandbox** filled (or, used to be filled) with black sand. So, one bucket can't equal one sandbox. And, apart from that, one bucket usually doesn't equal one sandbox in the real world.zzzz :)

-**Jonathan Y.**

Wait so we've established its equal right? So I was right? :)

-Sathvika R.

wooa! hold it!

i am utterly confused. as i previously stated a long time ago, black sand was more because the amount of black sand added was greater because the bucket was only black sand and nothing else. The other bucket of sand that was added to the black sand had mostly white sand, but had some black sand mixed into it, so it isnt 100% one color, like the other bucket. you **guys are getting tricked by the problem or it's just me!**

the problem is asking which is greater, the amount of black sand **added** to the white sand or the amount of white sand **added** to the black sand, or are they equal?

**the amount of black sand is obviously greater because when it was added, it was pure and without any white particles in it!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
then again i might be wrong…..
but i think im right.
when you put back the white sand how ever, it has some black particles in it, which makes up part of the total.**

-rohan kondetimmanahalli

**it can't be equal because 1 bucket of sand does not equal the entire sandbox, therefore im pretty sure im right**italic text

rohan kondetimmanahalli

What if we replaced it with Numbers? lets say a bucket full is 10% and a sand box is 100%, if u take 10% and add it to white then it becomes 110% stir that..its still 110%(is it?) then take another bucket full from that box of white sand and add it back to the black sandbox 110%-10% =100% (white box) 90%+10=100% ? soo they're equal ???

♫ Henry C ♫

**ur wrong henry** - read the question carefully

rohan!

Alright look, I'll make another example. Pretend the sandbox can hold 50 mL of sand, while the bucket can only hold 10 mL.

So when you scoop an entire bucket of sand into the white, it'll be 50 mL of white sand and 10 mL of black sand.

Meaning that when you scoop out another bucket of the mixture, it'll be 5/6 mL of white sand and 1/6 mL of black sand.

Therefore, it will be 8 mL of white sand and 2 mL of black sand back into the black sandbox.

Now when you pour the mixture in, that means that there's still 8 mL of black sand in the white sandbox and now 8 mL of white sand in the black sandbox. They are now equal.

And Rohan, you're reading the question wrong. It's asking if the amount of black sand added to the white sandbox is greater than the amount of white sand added to the black sandbox.

Which is greater, the amount of black sand added to the white sand or the amount of white sand added to the black sand, or are they equal?

P.S. You guys gotta stop forcing the lock out of other people's hands. Just let them edit and be patient.

—**John Y.**

A really good example John. Ever thought of being a teacher? Yeah…your right.

Rohan…this example works with all other kinds of numbers…your getting confused at the "perfectly mixed" part. It is there to throw you off.

STOP LOCKING PEOPLE!!!

thank you

^{Madhula}_{Madhula} Madhula ^{Madhula} _{Madhula}

**ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh!!!!!!!!!!!!!!!!!!!!!
i get it, ur right!
rohan**

**__//**SRY GUYS, IT APPEARS THAT IM THE ONE WHO READ THE QUESTION WRONG

THE ANSWSER IS THAT THEY'RE EQUAL-SRY!

OHAN KONDETIMMANAHALLIER**//__**

If every one agrees with me-

**Final Answer: It is equal**

Rohan Kondetimmanahalli

So my example was right? kinda..or right on? … the answer in equal.. are we sure…?

♫ Henry C ♫

yes u were right

**Final Answer: It is equal**

rohan

Well, your example was kinda… funky. Haha, because in the problem you didn't take into account of the percentage of white and black sand in the mixture. You just have 10% which doesn't tell us anything.

—**John Y.**

Hey at least I got close to the answer.. you just backed me up with a more solid example… thanks for saying that my example was "funky" …10%=amount of one bucket full that was taken out of a sandbox happy?

♫ Henry C ♫

the right answer is:

**it is equal**-rohan

agreed?

yes/ no

name

why if u say no

you guys should be thanking/agreeing with me (and perhaps john and sathvika). i'm the one who convinced them, and hopefully yall. and, i'm the one who got it right with perfect reasoning (yes, sathvika was right, but her reasoning/percentages were off)(but at least sathvika got the answer right). now, the answer should be clear to all that it is equal. thank you rohan for finally coming to the right side. if anyone disagrees, you are totally wrong. there is no way the black and white sand differ in their addition to the other sandbox. if anyone else posts, they should either be agreeing instantly or agreeing after having an epiphany. :)

-**Jonathan Y.**

Aren't you glad I swayed from everyone else's answers and said they were equal? :) Haha just joking. Anyways. I think my percentages were off because I didn't read the question correctly. So basically, they both are **equal** because you are just transferring sand back and forth the sand boxes right? So technically nothing gets "added" or "removed." Am I right? (By the way I like Henry's reasoning. It made it easier to understand.)

**So our final answer:
Equal.**

(Oh and John when i said new/old bucket, I meant what bucket you use to transfer [same size/shape/everything] however, the problem didnt specify:

1. first he took bucket1 and filled black sand and put it in the white sandbox to make mixed sand.

2.when he took a bucket of mixed sand to put back into the black sandbox to fill it up to 100% again, if he used the SAME BUCKET (bucket1) then there would be black particles thus making an imperfect mix

3. but what if he used a completely different CLEAN bucket [same size and shape] to transfer the mixed sand back to the black sandbox. Then wouldn't the results vary?

I'm not sure if I made much sense there. But yeah. Haha.)

-Sathvika R.

I guess we're assuming that the bucket dumped every single grain of sand into the sandbox so that the bucket would be clean. Otherwise, wouldn't the problem be invalid or just messed up?

I think this problem was more about comprehending the problem than solving the problem. >.>

—**John Y.**

John.. remember Alex had hours to stir the sand… i think he has enough time to make sure the bucket was completely empty?

so what now do we go up to Mr.Simmons and say"we're done!" … or just wait for the next question? HURRAY WE SOLVED THE QUESTION!!

♫ Henry C ♫

we got the most enthusiastic commentors out of all the periods…lolz.

O.O O.O O.O O.O O.O O.O O.O

woot! woot!

^{Madhula}_{Madhula} Madhula ^{Madhula} _{Madhula}

w00t- For those of you who are to lazy to read above and see what happened, we have finished the problem and come up with the anser:

**Equal**-Thanx all for there help

-Rohan

^{Done}_{Done}**DONE**_{Done}^{Done}

AHEM! we? if i didn't comment, no one would have payed attention to sathvika's post! Madhula was proving her wrong, then John posted the wrong answer again. but, yeah, the answer is equal. and henry, just like john said, it's more like HURRAY WE **COMPREHENDED** the problem. xD

-**Jonathan Y.**

Jonathan… just to let you know..i didn't read any of your posts..i just decided to write that percentage post because i thought of it ..i promise..i never even read your post..and fine **HURRAY WE COMPREHENDED THE PROBLEM**

♫ Henry C ♫

JONATHAN…READ IT!!! The 2nd or 3rd sentence mentions that i used Ayush's explanation from the 5th period discussion!!! Can you read things??? But thanks for mentioning so nobody skips it :D

But seriously Jonathan, ** Comprehend** it…its one of the beginning sentences…

Okay…i am really not sure guys if our answer is correct…

**think it is correct…but check out the other periods' they came to our mistaken conclusion…what if it is right?**

*I*

^{Madhula}_{Madhula}Madhula^{Madhula}_{Madhula}I've finally joined the wiki

-Mark L

I know you guys have already said that it's somehow equal, but i thought that there would be more black sand. He first got a bucket full of black sand and dumped it into the white sand and then mixed. So isn't the black sand like everywhere in the white sand so if you get a bucket of mixed sand there will be black sand also? When he got a bucket of mixed sand he dumped it into the black sand pit. So i thought that since the mixed sand has black sand, that sand was dumped into the black sand again. I see you guys have spent quite some time on this.

-David G.

I have no clue.

-Josh F.

lolz…it is equal.

Madhula A

The one who types last is lonely.

Brad S.