SAT question of the day
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To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange are mixed, what is the proportion of yellow dye in the new mixture? a. 3/16 b. 1/4 c. 11/30 d. 3/8 d. 7/12 -- From the SAT question of the day email I get as Ian signed me up as well to get these questions. Now, he figured this out (good for him) but it stumped me because I view the concept of "parts" to be abstract, making it impossible to equate "equal amounts of green and orange". I guess that's what I get for dealing with object oriented programming languages and always thinking too hard about math word problems. I guess if you consider "part" as a variable, like in: 5po=3pr + 2py 3pg=2pb + 1py then the "p" gets completely factored out. But in my thinking, the "parts" for making orange can be very different than the "parts" for making green. Which is another thing that I always had a problem with in word problems. If something can be completely factored out in the math, then why is it even used as a word in the problem? I've always attached meaning to the words in a math problem, when in reality, a lot of those words simple disappear in the math expressions. Wierd. Oh well, back to my abstractions and other imaginary worlds that I live in. Marc
The intrinsic assumptions here are that: (A) The same measure can and is applied to all colors. (B) The measure is additive, i.e. mixin A parts of X and B parts of Y gives (A+B) parts of whatever. Given that, the measure can be anything, a weight, a volume, the amount of paint Shlemiel the painter[^] uses on day 15. ('Part' can not be, however, the number of days Shlemiel needs to use the amount, since it's not linear, so mixing would not be additive) So, 5 parts of orange are contain 2 parts of yellow, so one part of orange dye contains 2/5 parts of yellow. Similary, 1 parts of green contain 1/3 part of yellow. 1 parts of yucky contain 1/2*(2/5+1/3) = 11/30 yellow. (c)
Math text questions always contain such assumptions, and recognizig them is an intrinsic part of solving such a question. A common problem of quite some bright minds is not recognizing the intrinsic assumptions, because their filter is crystal clear on the algebra/calculus stuff, but pithc black on the "common sense" part. In a bad education system, they simply need to know which question patterns are subject of this test, and which pattern is this? Simple and boring, because they see the pattern long before they understood the "real world problem" the question is trying to pose . In a good education system, they are immensely more challenged, and need some kind of reverse reasoning: (A) What kind of result is expected? (a value? a formula? a proof a solvability verdict?) (B) Consider all hidden assumptions necessary to arrive at such a result (C) Pick the assumptions that are most simple while requiring all - or the majority - of the information given. This contains two other hidden assumptions: the question is solvable with the information given, and there is no - or not much - redundant information. This is (often much) more complicated than applying common sense - because there's an infinite pool of possible assumptions. A simple fractional arithmetics question, solved in 30 seconds by some guy who needs five minutes to recognize the pattern, suddenly becomes open ended:
If we drop the "additive measure" requirement: Be O=O(R,Y) the number of parts of orange dye acquired from mixing R parts of red and Y parts of yellow. Similary, define G=G(B,Y) and U=U(O,G). this gives U = U
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How I solved the problem: Yellow = 2/5 of Orange dye. Yellow = 1/3 of Green dye. 1/2 Orange + 1/2 Green = new mixture. New mixture contains (1/2 * 2/5) + (1/2 * 1/3) yellow. New mixture contains 11/30 yellow. I've always been good at visualizing and solving math problems in my head, but I haven't really had to do that much of it recently, with me mostly doing WPF user interface design as of late.
Show off... I did it as (2/5 + 3/5) + (1/3 + 2/3) == (6/15 + 9/15) + (5/15 + 10/15) looking at the numerators only, I see 30 parts, 11 of which are yellow.
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Andy Brummer wrote:
Anyway, unless you are measuring flour on Earth, salt on Venus and water on Mars, it's going to workout just fine.
True but the end result is often a desired volume of bread "loaves" so I guess you'd have to experiment a bit to find out how to get 10 loaves out of an earth bread formula when you're on Mars. Hmm...now that I think about it the bread would probably rise at a different rate in different gravity and air pressure environments as well. I'd really like to send up a starter ball of dough with the space shuttle and have them put it somewhere out of the way with no air currents so it just floats there as it expands. Then put it in the airlock and pump out the air, it would probably expand to the entire inside of the lock. :)
When everyone is a hero no one is a hero.
Why bake bread in space anyway, you have freeze dried ice cream and tang. Mmmmmmmmmmmmmm. Tang.
This blanket smells like ham
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Andy Brummer wrote:
It's used whenever you are talking about ratios of quantity, like in chemistry or baking. It doesn't have to say that explicitly because that's what the word means.
Interesting. Well. Yet again, I discover how warped my view of the world is. :) Thanks! Nice to know I can learn something 30 years after it was important to learn it. :-D Marc
You never know when you'll have to make concrete with cement, sand, gravel and water. You already have solar power, you're halfway to having your own compound already.
This blanket smells like ham
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Why bake bread in space anyway, you have freeze dried ice cream and tang. Mmmmmmmmmmmmmm. Tang.
This blanket smells like ham
Andy Brummer wrote:
Why bake bread in space anyway
Bite your tongue! Even prospectors on the gold rush trail to the Yukon would bake bread on the side of the trail when they stopped for the night, the cook would keep the sourdough starter in his pocket so it wouldn't freeze. When Richard Branson gets his space hotel in orbit up and running, I'll be the dude making a fortune on my microgravity bread machine! ;)
When everyone is a hero no one is a hero.
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Show off... I did it as (2/5 + 3/5) + (1/3 + 2/3) == (6/15 + 9/15) + (5/15 + 10/15) looking at the numerators only, I see 30 parts, 11 of which are yellow.
You did the math differently, but it seems like you did the visualization of the problem in nearly the same way. The trick to solving these word problems is to turn the problem into a picture in your head of what's actually going on (and then use that picture to decide which math steps to take). Picture first, formula afterwards. It's when people try to do formula first instead that word problems get hard.
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Andy Brummer wrote:
Why bake bread in space anyway
Bite your tongue! Even prospectors on the gold rush trail to the Yukon would bake bread on the side of the trail when they stopped for the night, the cook would keep the sourdough starter in his pocket so it wouldn't freeze. When Richard Branson gets his space hotel in orbit up and running, I'll be the dude making a fortune on my microgravity bread machine! ;)
When everyone is a hero no one is a hero.
Soufflé
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To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange are mixed, what is the proportion of yellow dye in the new mixture? a. 3/16 b. 1/4 c. 11/30 d. 3/8 d. 7/12 -- From the SAT question of the day email I get as Ian signed me up as well to get these questions. Now, he figured this out (good for him) but it stumped me because I view the concept of "parts" to be abstract, making it impossible to equate "equal amounts of green and orange". I guess that's what I get for dealing with object oriented programming languages and always thinking too hard about math word problems. I guess if you consider "part" as a variable, like in: 5po=3pr + 2py 3pg=2pb + 1py then the "p" gets completely factored out. But in my thinking, the "parts" for making orange can be very different than the "parts" for making green. Which is another thing that I always had a problem with in word problems. If something can be completely factored out in the math, then why is it even used as a word in the problem? I've always attached meaning to the words in a math problem, when in reality, a lot of those words simple disappear in the math expressions. Wierd. Oh well, back to my abstractions and other imaginary worlds that I live in. Marc
Somehow, this will be used as an interview question for some poor programmer interview-e
MrPlankton
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The intrinsic assumptions here are that: (A) The same measure can and is applied to all colors. (B) The measure is additive, i.e. mixin A parts of X and B parts of Y gives (A+B) parts of whatever. Given that, the measure can be anything, a weight, a volume, the amount of paint Shlemiel the painter[^] uses on day 15. ('Part' can not be, however, the number of days Shlemiel needs to use the amount, since it's not linear, so mixing would not be additive) So, 5 parts of orange are contain 2 parts of yellow, so one part of orange dye contains 2/5 parts of yellow. Similary, 1 parts of green contain 1/3 part of yellow. 1 parts of yucky contain 1/2*(2/5+1/3) = 11/30 yellow. (c)
Math text questions always contain such assumptions, and recognizig them is an intrinsic part of solving such a question. A common problem of quite some bright minds is not recognizing the intrinsic assumptions, because their filter is crystal clear on the algebra/calculus stuff, but pithc black on the "common sense" part. In a bad education system, they simply need to know which question patterns are subject of this test, and which pattern is this? Simple and boring, because they see the pattern long before they understood the "real world problem" the question is trying to pose . In a good education system, they are immensely more challenged, and need some kind of reverse reasoning: (A) What kind of result is expected? (a value? a formula? a proof a solvability verdict?) (B) Consider all hidden assumptions necessary to arrive at such a result (C) Pick the assumptions that are most simple while requiring all - or the majority - of the information given. This contains two other hidden assumptions: the question is solvable with the information given, and there is no - or not much - redundant information. This is (often much) more complicated than applying common sense - because there's an infinite pool of possible assumptions. A simple fractional arithmetics question, solved in 30 seconds by some guy who needs five minutes to recognize the pattern, suddenly becomes open ended:
If we drop the "additive measure" requirement: Be O=O(R,Y) the number of parts of orange dye acquired from mixing R parts of red and Y parts of yellow. Similary, define G=G(B,Y) and U=U(O,G). this gives U = U
peterchen wrote:
(A) The same measure can and is applied to all colors.
That's helpful, but not required.
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To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange are mixed, what is the proportion of yellow dye in the new mixture? a. 3/16 b. 1/4 c. 11/30 d. 3/8 d. 7/12 -- From the SAT question of the day email I get as Ian signed me up as well to get these questions. Now, he figured this out (good for him) but it stumped me because I view the concept of "parts" to be abstract, making it impossible to equate "equal amounts of green and orange". I guess that's what I get for dealing with object oriented programming languages and always thinking too hard about math word problems. I guess if you consider "part" as a variable, like in: 5po=3pr + 2py 3pg=2pb + 1py then the "p" gets completely factored out. But in my thinking, the "parts" for making orange can be very different than the "parts" for making green. Which is another thing that I always had a problem with in word problems. If something can be completely factored out in the math, then why is it even used as a word in the problem? I've always attached meaning to the words in a math problem, when in reality, a lot of those words simple disappear in the math expressions. Wierd. Oh well, back to my abstractions and other imaginary worlds that I live in. Marc
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Andy Brummer wrote:
Why bake bread in space anyway
Bite your tongue! Even prospectors on the gold rush trail to the Yukon would bake bread on the side of the trail when they stopped for the night, the cook would keep the sourdough starter in his pocket so it wouldn't freeze. When Richard Branson gets his space hotel in orbit up and running, I'll be the dude making a fortune on my microgravity bread machine! ;)
When everyone is a hero no one is a hero.
John C wrote:
the cook would keep the sourdough starter in his pocket so it wouldn't freeze.
Sounds yummy.
This blanket smells like ham
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peterchen wrote:
(A) The same measure can and is applied to all colors.
That's helpful, but not required.
Is it not?
We are a big screwed up dysfunctional psychotic happy family - some more screwed up, others more happy, but everybody's psychotic joint venture definition of CP
blog: TDD - the Aha! | Linkify!| FoldWithUs! | sighist -
I think the more important question is...who the crap would want to mix green and orange? What puke color is that?
Kschuler wrote:
I think the more important question is...who the crap would want to mix green and orange? What puke color is that?
umm, err, CodeProject? :(
-Sean ---- ????? ?????????
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Kschuler wrote:
I think the more important question is...who the crap would want to mix green and orange? What puke color is that?
umm, err, CodeProject? :(
-Sean ---- ????? ?????????
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To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange are mixed, what is the proportion of yellow dye in the new mixture? a. 3/16 b. 1/4 c. 11/30 d. 3/8 d. 7/12 -- From the SAT question of the day email I get as Ian signed me up as well to get these questions. Now, he figured this out (good for him) but it stumped me because I view the concept of "parts" to be abstract, making it impossible to equate "equal amounts of green and orange". I guess that's what I get for dealing with object oriented programming languages and always thinking too hard about math word problems. I guess if you consider "part" as a variable, like in: 5po=3pr + 2py 3pg=2pb + 1py then the "p" gets completely factored out. But in my thinking, the "parts" for making orange can be very different than the "parts" for making green. Which is another thing that I always had a problem with in word problems. If something can be completely factored out in the math, then why is it even used as a word in the problem? I've always attached meaning to the words in a math problem, when in reality, a lot of those words simple disappear in the math expressions. Wierd. Oh well, back to my abstractions and other imaginary worlds that I live in. Marc
Just fill in your own unit of measurement...
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Amusingly enough, if all of us college graduates had to retake the SAT's now, we'd probably all fail and never get admitted a second time round :)
¡El diablo está en mis pantalones! ¡Mire, mire! Real Mentats use only 100% pure, unfooled around with Sapho Juice(tm)! SELECT * FROM User WHERE Clue > 0 0 rows returned Save an Orange - Use the VCF! VCF Blog
Maybe, but after they watered down the SAT several years ago I bet I could still ace the thing - drunk.
"A Journey of a Thousand Rest Stops Begins with a Single Movement"
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You never know when you'll have to make concrete with cement, sand, gravel and water. You already have solar power, you're halfway to having your own compound already.
This blanket smells like ham
right. yellow-green concrete is my favorite one. :)
Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips: - before you ask a question here, search CodeProject, then Google; - the quality and detail of your question reflects on the effectiveness of the help you are likely to get; - use PRE tags to preserve formatting when showing multi-line code snippets.
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I think the more important question is...who the crap would want to mix green and orange? What puke color is that?
haven't you tried it by now? they are on about it for hours already....
Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips: - before you ask a question here, search CodeProject, then Google; - the quality and detail of your question reflects on the effectiveness of the help you are likely to get; - use PRE tags to preserve formatting when showing multi-line code snippets.
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Show off... I did it as (2/5 + 3/5) + (1/3 + 2/3) == (6/15 + 9/15) + (5/15 + 10/15) looking at the numerators only, I see 30 parts, 11 of which are yellow.
But that is o so wrong. how can
0 == 0prove or solve anything? :wtf: you should have used real numbers here.Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips: - before you ask a question here, search CodeProject, then Google; - the quality and detail of your question reflects on the effectiveness of the help you are likely to get; - use PRE tags to preserve formatting when showing multi-line code snippets.
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Is it not?
We are a big screwed up dysfunctional psychotic happy family - some more screwed up, others more happy, but everybody's psychotic joint venture definition of CP
blog: TDD - the Aha! | Linkify!| FoldWithUs! | sighistBy which I mean that different units may be used at each step.