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. Joann scoops a full bucket of the black sand and pours it into the white sand. Joann stirs this mixture for hours (shouldn't she be reading a book?) until the black and white sand are perfectly mixed. Joann 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…

awesome im first unless someone posts faster then me…
all right what i think:
I think that the amoutn of black sand added to the white sandbox is greater because if you put a bucket of the mixed sand into the white bucket, then the bucket of mixed sand will have to have some black sand, and since the bucket of black sand is 100 percent black sand, and the bucket of mixed sand has less than 100 percent white snad due to the mixing of the blakc sand, i confirm my answer.
------Joseph L.

  • I think that they are the same because the amount of white sand in the black sand that will fill the sandbox back up to the original amount must be the same amount of black sand that's missing. The amounts must be the same if you end up with the same amount in both containers.
  • Simply put, both sandboxes started out with the same amount, right? so if they both end up with the same amount, they basically swapped a set amount, or the bucketfull.
  • I can debate this with anyone who disagrees.

-James D.

What are you talking about? Does the dude get a bucket from each sand box? And there can be particles of blakc sand in the white sand.
JOseph L.

Oh! When you pour the mixed sand back you put some of the black particles back so, in reality, your subtracting the amount you put in the white originally so… You're both wrong! You put more white in the black because you put some black back making the white amount more than the black.
:] Katie B.

actually no. because the blakc particles in the bucket subtract the white particles you're supposed to that means it's less than 100 percent. and the black to the white is 100 percent.
joseph l.

notice it said added. not the amount in the sand box after. i almost agrreed with you though.
Joseph L,

Look, we can agree that they started and ended with the same amount, right? Because no units are given, we can pretend there's gallon in each sandbox. And we can also pretend the bucketfull is a gallon. You take the gallon of white sand, leaving nothing left in that sandbox, and put in in the other, which now has 2 gallons. Once you mix it up, It's 50% white for 50% black, right? Once you take a gallon back, it's supposed to be a 50/50 mixture. So now both boxes have 50% white and 50% black, which indicates that they are equal.
-James D.

"…or the amount of white sand added to the black sand…"
I got confused at that part! Is it talking about the mixed sand, or was there a part of the problem where they added white sand to black sand and I totally missed it?
Your favorite classmate, Marianna H. :)

The amount of black sand has to be more because when she added the bucket of black sand, she added a bucket of whole black sand. But when she added the white sand, it was still one bucket, but it wasn't a whole bucket of just white sand like before
- Yash T.

I agree with Yash! The amount of black sand does have to be greater because she put a whole bucket of black sand into the white, so when she poured the bucket of mixture in, there had to be at least less than a bucket of white sand in the bucket! Kinda true though!!

it says added… not the amount after.

joseph l.

wiat james is rite. cause you subtract the black you take back in the mixed sand from the full bucket of black in the start. credit to jonathan. he helped a truckload. 1st period has like a 100 posts. let's beat em.

joseph l.

final ans: THEY ARE EQUAL :D:D:D:D:D:D btw im trying to get my karma level up to this zen master thing. so dont bother reading the useless ones.

joseph l.

here's an example if you are confused:
say each sandbox of sand holds 40 ml. and the bucket holds 10 ml.
transfer 10 ml of black to white.
30ml in black
50 ml in white- 40 ml white and 10ml black
so when you fill the bucket again: it's 1/5 black and 4/5 white. which is 2 ml blakc and 8 ml white.
transfer it back to blacksandbox. so then you subtract the 2 ml black from the 10 ml you transferred to the white sandbox in the beginning. 10 - 2 = 8. 8=8. :D

JOsphe l.

Man! could you guys try to spell things correctly?! Gosh! That makes it so much harder to understand! As if it weren't complicated enough! Anyway I think it could be equal but… I don't know. It really depends on how you look at it. I see it that the white sand added to the black is more because you put back some of the black. Yash and Casey see it as having more black sand because they see that you initially add more black making it so that the black is re no matter what. And James and Joseph see it as being equal 'cause they are all official with they're fractions and mathematical stuff. I know this didn't help anyone but I hate it when people argue so keep an open mind…
Katie B. :]

all rite all what's your argument? besdies can you guys post more? i feel lonely with my 4 straight posts.

joseph l

o sweet my karma level is medium!! my hard work paid off

jopseh l.

What's a "karma level"? Ya no comprendi(with accent on i) que joseph esta(accent) hablando. And its your fault your lonely you know.
Katie B. :)

hey yo. dont speak spanish on me. it probably means im a loser. rite? lemme see. ya no comprendi= i dont understand? que joseph esta= accent hablando= disney world? a karma level is like how many posts you have. i posted alot so im a medium

joseph l. im such a nerd

-.- somebody told me what that meant. i kno nobody's gonna read this but im just gonna pout here. it means that im a loser and that i have no friends? is that rite?

joseph l.

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License