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quote:

Originally posted by DigiNut That really depends whether or not Billy is running an industrial assembly line. I mean, it's pretty unlikely that he has the equipment sitting around in his basement to melt and fuse copper with perfect efficiency and without introducing any impurities. So I'd have to assume he's working at a plant somewhere. Assuming that, we still need to know if it's a clean room, like a fab, or a regular factory where the copper slabs have no doubt picked up all sorts of dirt, and the melting process probably leaves a copper residue behind. Now, since the question explicitly states "the resulting piece", it also clearly suggests a freezing process. Does it go into a freezer, sealed, or is it just left sitting around until it solidifies? If memory serves, copper doesn't sublimate, but the impurities might at the right atmospheric temperature, which means that the resulting solid might actually be slightly more pure than the original liquid. Finally, how is the determination of purity being made? It's easy enough to weigh the thing, but in order to determine the purity you usually have to melt it down or distill it, which seems to be a pointless exercise here after making the new alloy. And if Billy had to melt down the original two samples just to find out the purity, how can we be sure that he didn't lose some copper in that process, before he even started combining them? Are we assuming a specific loss rate here or are these ideal, perfect (i.e. imaginary) conditions? More to the point, if Billy already has a scale, which he would have needed to weigh the final sample, why didn't he just weigh the original two samples in the first place instead of going through all this ridiculous hassle?

LOL...

My math...

I worked the percentages...

Copper...

60% of 51% is 30.6% of 400g is 122.4g...

40% of 51% is 20.4% of 400g is 81.6g...

And the alloy...

40% of 49% is 19.6% of 400g is 78.4g...

60% of 49% is 29.4% of 400g is 117.6g...

Add the totals...

122.4 + 78.4 = 200.8

81.6 + 117.6 = 199.2


200.8g + 199.2g = 400g

x = mass of alloy w/ 60% copper
y = mass of allow w/ 40% copper

Total mass of copper = 51% of 400g = 204g
Mass of copper in x = 60% of x = 0.60x
Mass of copper in y = 40% of y = 0.40y

Assuming, no constituent of the alloy is lost,
x + y = 400g
and
0.60x + 0.40y = 204

Solving for x and y gives:

x = 220g
y = 180g

quote:

Originally posted by Search&Rescue x = mass of alloy w/ 60% copper y = mass of allow w/ 40% copper Total mass of copper = 51% of 400g = 204g Mass of copper in x = 60% of x = 0.60x Mass of copper in y = 40% of y = 0.40y Assuming, no constituent of the alloy is lost, x + y = 400g and 0.60x + 0.40y = 204 Solving for x and y gives: x = 220g y = 180g

Yes that answer does seem a lot easier to swallow...

But where my math is faulted is what I want to know....

quote:

Originally posted by ChemEnhanced I could just imagine some kid at school writing that down on a test because he didn't know the answer.

In all seriousness, it's a better answer than the obvious one. I'd give bonus marks for it. In the real world, you don't work under ideal conditions; more importantly, I wish more people could look at a complicated, long-winded process and say "Hey, there's a WAY simpler solution here."

This is why I always hated school. Contrived problems, oversimplified solutions. (And I was an engineer)

quote:

Originally posted by ChemEnhanced now look in the back of the math book and get the answer Copper = 204 Alloy = 196 60%copper (122.4) + 40%alloy (78.4) = 200.8 40%copper (81.6) + 60%alloy(117.6) = 199.2

in every number you have in parentheses, you have assumed the original mass of the alloy to be either 100% copper (when you're calculating the mass of the copper in each) or 0% copper (when you're calculating the mass of contituents other than copper in each)

quote:

Originally posted by Search&Rescue x = mass of alloy w/ 60% copper y = mass of allow w/ 40% copper Total mass of copper = 51% of 400g = 204g Mass of copper in x = 60% of x = 0.60x Mass of copper in y = 40% of y = 0.40y Assuming, no constituent of the alloy is lost, x + y = 400g and 0.60x + 0.40y = 204 Solving for x and y gives: x = 220g y = 180g

your formula looks good to me....can you break down the calculations to get x and y.....its been way too long since I've had to do this type of math....and I actually use to be good at it

quote:

Originally posted by ChemEnhanced can you break down the calculations to get x and y.....

are you being serious? Because I can't tell

quote:

Originally posted by Search&Rescue are you being serious? Because I can't tell

I am being serious....I haven't done problem solving like this probably 15 years

I am trying to work through it...but keep getting stuck.

quote:

Originally posted by ChemEnhanced I am being serious....I haven't done problem solving like this probably 15 years I am trying to work through it...but keep getting stuck.

well, in that case:
you re-arrange any one unknown and express the other in terms of this
e.g. x + y = 400
so x = 400 - y

then you got your second equation in terms of x and y
substitute x = 400 - y into your second equation, re-arrange the terms and solve for y. Then solve for x which is just = 400 - y

..and that's just one way of solving linear equations

quote:

Originally posted by Search&Rescue well, in that case: you re-arrange any one unknown and express the other in terms of this e.g. x + y = 400 so x = 400 - y then you got your second equation in terms of x and y substitute x = 400 - y into your second equation, re-arrange the terms and solve for y. Then solve for x which is just = 400 - y

yeah...I get to .6(400-y) + y = 204 without a problem...but this is where I get lost solving for y. I am just forgeting the rules....like I said...its been way too long.

quote:

Originally posted by Search&Rescue in every number you have in parentheses, you have assumed the original mass of the alloy to be either 100% copper (when you're calculating the mass of the copper in each) or 0% copper (when you're calculating the mass of contituents other than copper in each)

I don't think he is...

He's saying that 60% of the 204g is copper...122.4g...etc

quote:

Originally posted by Search&Rescue ..and that's just one way of solving linear equations

And can you please tell me where mine was wrong?????

quote:

Originally posted by VDub I don't think he is... He's saying that 60% of the 204g is copper...122.4g...etc

his formula is correct....I just can't figure out the long form of how to do it right now.

quote:

Originally posted by ChemEnhanced his formula is correct....I just can't figure out the long form of how to do it right now.

Yah I agree it's correct....

I just can't see where I screwed up...

quote:

Originally posted by ChemEnhanced yeah...I get to .6(400-y) + y = 204 without a problem...but this is where I get lost solving for y. I am just forgeting the rules....like I said...its been way too long.

try this then since its a little less tedious:

1) x + y = 400
2) 0.60x + 0.40y = 204

multiple 1) by 0.60 (each term on the left and right hand side)
you get:
1) 0.60x + 0.60y = 400 x 0.6

now subtract 1) from 2). you get:
0.20y = (400 x 0.6) - 204
divide both sides by 0.20 to get your final value for y

quote:

Originally posted by VDub I don't think he is... He's saying that 60% of the 204g is copper...122.4g...etc

that's the problem.
you have to take 60% of the total mass of the alloy which is not 204g. That's really the unknown - what you're trying to find

204g is the sum of the copper content in BOTH alloys

You guys were screwing up because you calculating the %60/%40 from the 204g.......when the question was asking about the ORIGINAL pieces, not the final piece.

Read the question again, and then look at your calculations. You should not be basing it on the final 204g........

quote:

Originally posted by cammaxwell You guys were screwing up because you calculating the %60/%40 from the 204g.......when the question was asking about the ORIGINAL pieces, not the final piece. Read the question again, and then look at your calculations. You should not be basing it on the final 204g........

I got it figured out now....I was making things more difficult then they needed to be.

quote:

Originally posted by cammaxwell You guys were screwing up because you calculating the %60/%40 from the 204g.......when the question was asking about the ORIGINAL pieces, not the final piece. Read the question again, and then look at your calculations. You should not be basing it on the final 204g........

Ahhhhhhh.....

Ok I see.......

Frickin idiot.....

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