Problem 1

## 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. Asfiya scoops a full bucket of the black sand and pours it into the white sand. Asfiya stirs this mixture for hours (she should be practicing her algebra) until the black and white sand are perfectly mixed. Asfiya 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

Hm. I think it's the amount of black sand added to the white sand, because he poured in a whole bucket! For pouring back, he would only have some white sand in the bucket because it's mixed with the black sand… so shouldn't it be the amount of black sand added to the white sand is greater?
-Valerie C.

Wow! Ok…. I agree with Val. :) I think the amount of black sand added was more. She adds a bucket filled with black sand to the white sandbox and when she mixes them together the white sandbox doesn't have just white sand anymore. So when she adds a bucket of the mixture to the black sandbox….. she isn't adding all white sand. But when she added the black sand the bucket was filled with only black sand. So the amount of black sand added was more. Does that make sense? :]
~ shreeya p. =P

Haha. Yes Shreeya, it does make sense :P
Okay, I am fairly certain the amount of black sand added to the white sand is greater because of these main points:
1. Asfiya gets one bucket of black sand from a black sandbox and pours it into a white sandbox
2. She[?] mixes the sand until it is "perfectly mixed"
3. She pours one bucket of white/black sand back into the black sandbox, therefore making the two equal in amount of sand

So imagine a bucket of black sand. And now imagine that same bucket with white/black sand. You can clearly tell that the black sand in the black bucket is greater than the amount of white sand in the mixed bucket.
Yes, Asfiya does give SOME of the black sand back to the black sandbox, but it shouldn't drastically change the results. The sandbox has to be AT LEAST hold an amount > one bucket, because it has to be able to hold the sand in the bucket + the amount that was originally there.
However, we may be wrong because we don't know the size of the sandbox. Generally, a sandbox is pretty big, but we don't know for sure about Asfiya's sandbox.
Oh well. I still think that the amount of black sand>white sand :)

-Valerie C. (hope this wasn't too confusing…)

Nope not confusing at all! It was a great way to explain. More people from our class need to get on here! lol!
~ shreeya p. =P

I also agree with Shreeya and Valerie. I think the amount of black sand the used would be greater since he some of it is mixed in the white. :D

-Christina O.

Hey guys you might wanna check out the other periods!!!!!! period one thinks its equal but i havn't looked at their explanations very closely. but i think we could try checking them out. and some other periods were saying it is way too easy. sooo…. idk! spazspazspaz! i hope more people answer this. it would help a lot! ahhhhhh! xD
☻§hreeya p.☺

So I read some of the other periods and a lot had a mistake thinking that "perfectly mixed" meant that the bucket had 50% black and 50% white. However, that's not the case… but I tried to do an example to prove that black was more… but instead it turned out equal… o.O
Say a sandbox holds 100 grains of sand, and a bucket 10. The 10 grains of black sand is "perfectly mixed" with the white, so the total in the sandbox 110. If it was perfectly mixed, 1 out of every 10 grains of sand is black, so if you scoop a bucket to pour it back, there would be one black grain being poured back, and 9 white grains. And the 10 black grains you poured into the white sandbox is now 9, because you poured back 1 grain into the black sandbox…
?
huh… I'm confused now x)
What do you guys think?
-Valerie C.

I agree with you guys that the amount of black sand is greater than the amount of white sand. I think this because like Valerie said, he poured in a whole bucket of black sand, but the problem is we don't know what the exact definition of perfectly mixed is. I don't think it means 50% black and 50% white. Or does it? When he says he scoops a full bucket of the black sand and pours it into the white sand, is he reffering to pouring one scoop of black sand into the white sand box? If so I don't think wecan we make that comparison because we don't know the size of the sand box or the scoop? just an idea,but I still agree with you guys.

-Courtney H

ok! wow! very confusing! i think we should wait for more answers that way we might get an idea where to start with. but i still think that the amount of black is greater. time to think out of the box!!!!!! gah!
§hreeya p.

Hey shreeya its ok more ppl will come to the site eventually! But youre all right, especially Val. It has to be that more black sand than white because as you said, the mixture was "perfect". If it is perfect, then there has to be a good ratio of black to white sand, but theres still more white than black being poured in by the bucket. So if the bucket was filled to the same amount, then no matter how much white sand was put in it, more black sand had already been added
PS- ppl stop overriding the lock!
- Rafa R

No wait! never mind! Valerie the example you showed actually makes sense! if, like we both said, the ratio of white to black is perfect in the mix, then when you pick up a bucketful of it and pour it into the black bucket, you would be balancing out the amount of sand. I think what we really had to figure out was the total ratio of white to black and black to white was the same for both buckets. So I agree with the example, theyre equal…. o.O
- Rafa R

Ya! omg! that does make sense. wow. at first i was very confused then i read rafael's and went back to val's and it made more sense. so what you guys are trying to say is that when we pour back the mixture the one grain that is poured back basically makes the other side equal. but then won't there be more black left in the white sandbox? because if we do that and we pour in some of the mixture into the black sandbox we will end up with an uneven amount. one sandbox will have more than the other. w8 i think i confluzed myself!!!!! uh -oh! does th is make any sense?! o.o
§hreeya p.

wait!!!!! never mind! disregard the last couple sentences i wrote in the previous paragraph. i confused myself. val and rafael are correct! yea go val and rafael! ☺☺☺☺☻☻☻☻
so our answer is equal rite?
~ §hreeya p.

:P hehe. okay. so our answer is equal?
-Valerie C.

yupsies!!! does everyone else agree? with equal?
~§hreeya p.

Yeah agree that makes sense.
-Courtney H

Okay so we all agree….well at least all of us that actually signed up so far… that for our final answer well say that theyre equal? Okay!
-Rafa R

Yes i agree that the ammount of sand in each box is equal too because its like having 2 boxes with lets say 2 kg of sand in each. Then it sais scoop a bucket full so lets say that scoop was 1kg. So now we have a bucket containing 1 kg of sand and the other with 3 kg of sand. THEN it sais that she took another bucket full of sand from the mixed sand (which is the bucket with 3 kg) and to add it to the other box of sand. SO then you subtract 1 kg from the mixed and add it to the bo of sand with 1 kg and theyhave equal ammounts of sand :)
-Jonathan T.

page revision: 28, last edited: 12 May 2009 02:58