OT: Math - Page 3 - Hoops Dynasty

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Posted by isack24 on 9/18/2012 11:16:00 PM (view original):
50y + 250 = 125
50y = -125
y = -2.5

Solving

10 x 5 x (-2.5 + 5) = 125
50 x (2.5) = 125
125 = 125

I think it helps to put in the extra multiplication sign :)

10 * 5(Y+5) = 125

10 * (5Y + 25) = 125
50 Y + 250 = 125
50 Y = -125
Y = -125/50
Y = -2.5

OK, good.

Now... treating this the same way and distributing the same way...

100 ÷ Y (2+3) = 10
100 / Y (2+3) = 10
100 / (2Y + 3Y) = 10
100 / 5Y = 10
multiply both sides by 5Y
100 = 5Y * 10
100 = 50Y
2 = Y

EDIT: I think.

9/18/2012 11:29 PM (edited)

isack24

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Yeah, but I didn't distribute that way (sorry, didn't show my work well).

10 x 5(y+5) = 125
50(y + 5) = 125
and you know the rest.

Problem is, because you are multiplying twice, distributing doesn't matter. You get to -2.5 any way you do it (properly or improperly, although I'm not sure we've established what's truly proper). You can do it in any order. Not the case when you're mixing in division.

9/18/2012 11:31 PM

coach_billyg

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what the hell are you guys talking about? is there still a question? i couldn't make it through all this. but there is absolutely no ambiguity to these kinds of questions.

9/19/2012 12:00 AM

coach_billyg

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Posted by sol_phenom3 on 9/18/2012 7:49:00 PM (view original):
Al, that's wrong. It's 100 DIVIDED by Y(2+3) = 10. Not 100 MINUS Y(2+3).

Regardless, Y is 2. It's simple math. 100 / 2(2+3) = 10. Because 2(2+3) is either 2*5 or 2*2 + 2*3, either way, that gives you 10. 100 / 10 = 10. Problem solved.

this is wrong too. the answer to the original question is 50. 100 / 50 * 5 = 10. order of operation follows as PEMDAS, breaking ties left to right. you do the 100/Y FIRST. so 100/Y*5 = 10 is the same as 100/Y = 50, 100 = 50Y, 100/50 = Y, 2 = Y

9/19/2012 12:02 AM

coach_billyg

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Posted by zbrent716 on 9/18/2012 9:50:00 PM (view original):
Posted by sol_phenom3 on 9/18/2012 7:49:00 PM (view original):
Al, that's wrong. It's 100 DIVIDED by Y(2+3) = 10. Not 100 MINUS Y(2+3).

Regardless, Y is 2. It's simple math. 100 / 2(2+3) = 10. Because 2(2+3) is either 2*5 or 2*2 + 2*3, either way, that gives you 10. 100 / 10 = 10. Problem solved.

OK, so if Y=2 there... solve this:

6 ÷ 2 (1+2) =

this is the same as saying 6 / 2 * 3 = X, solve for X. left to right, you do 6/2 first, which is 3. 3*3 is then 9.

9/19/2012 12:03 AM

coach_billyg

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Posted by isack24 on 9/18/2012 11:17:00 PM (view original):
I certainly agree about the ambiguity, but unless there is some special rule of which I'm not aware, I think these are the right answers.

there is no special rule. its simply, PEMDAS, left to right. parens always get resolve first, followed by exponents, followed by mult/division (same level, break ties left to right), followed by addition/subtractions (same level, break ties left to right)

9/19/2012 12:08 AM

coach_billyg

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Posted by zbrent716 on 9/18/2012 11:09:00 PM (view original):
Posted by isack24 on 9/18/2012 11:03:00 PM (view original):
Yeah, I would think 50 is the answer to the first.

I think the natural tendency is to distribute y to the parenthetical and create a 100 / 5y = 10 situation.

But it should read just like hughes wrote it.
10 * 5(Y+5) = 125

Y=?

the correct way to do this:
10 * 5 (Y + 5) = 125

for clarity:
10 * 5 * (Y + 5) = 125

50 * (Y + 5) = 125

50Y + 250 = 125

50Y = -125

Y = -2.5

9/19/2012 12:12 AM

coach_billyg

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Posted by zbrent716 on 9/18/2012 11:29:00 PM (view original):
Posted by isack24 on 9/18/2012 11:16:00 PM (view original):
50y + 250 = 125
50y = -125
y = -2.5

Solving

10 x 5 x (-2.5 + 5) = 125
50 x (2.5) = 125
125 = 125

I think it helps to put in the extra multiplication sign :)

10 * 5(Y+5) = 125

10 * (5Y + 25) = 125
50 Y + 250 = 125
50 Y = -125
Y = -125/50
Y = -2.5

OK, good.

Now... treating this the same way and distributing the same way...

100 ÷ Y (2+3) = 10
100 / Y (2+3) = 10
100 / (2Y + 3Y) = 10
100 / 5Y = 10
multiply both sides by 5Y
100 = 5Y * 10
100 = 50Y
2 = Y

EDIT: I think.

you are doing it wrong, the second part. like i did in the last one, put in the multiplication simple to keep from confusing yourself

100 / Y (2 + 3) = 10
is the same as
100 / Y * (2 + 3) = 10
or
100 / Y * 5 = 10

order of operations, mult and division are the same, go left to right

(100 / Y) * 5 = 10
(100 / Y) = 10 / 5
100 / Y = 2
100 = 2Y
Y = 50

9/19/2012 12:13 AM

darnoc29099

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Apples and oranges are being discussed here. You don't use PEMDAS when solving for a variable, like the 100 / y(2+3) = 10 example. That's an equation where you need to isolate the variable, Y. All the math has already been laid out, and the answer is 2.

6 / 2(1+2) is an order of operations problem, where the PEMDAS acronym would apply (which says in order from left to right, you simplify Parentheses, Exponents, Multiplication and Division (simultaneously, starting from the left), then Addition and Subtraction (again, simultaneously)). This becomes 6 / 2 *3...3*3 = 9.

9/19/2012 12:13 AM

coach_billyg

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Posted by darnoc29099 on 9/19/2012 12:13:00 AM (view original):
Apples and oranges are being discussed here. You don't use PEMDAS when solving for a variable, like the 100 / y(2+3) = 10 example. That's an equation where you need to isolate the variable, Y. All the math has already been laid out, and the answer is 2.

6 / 2(1+2) is an order of operations problem, where the PEMDAS acronym would apply (which says in order from left to right, you simplify Parentheses, Exponents, Multiplication and Division (simultaneously, starting from the left), then Addition and Subtraction (again, simultaneously)). This becomes 6 / 2 *3...3*3 = 9.

you are absolutely and completely wrong (no offense). you DO use pemdas to isolate for y, and i have no idea where the notion comes from that you would not. if you didn't, it would make no sense. for example, if you plug 2 into the original equation to see if it equals 10, you would obviously use pemdas, so you would get

100 / y (2+3) = ?
100 / 2 (2 + 3) = ? (substitution, y = 2)
100 / 2 * 5 = ? (do the parenthesis first
50 * 5 = ? (left to right)
250 = ?

you are supposed to get 10, this obviously does not work. pemdas always applies in these kinds of math problems. having variables or not has *absolutely* nothing to do with it.

if you want to isolate Y, here is how you do it. ill do it formally so you can follow every exact step in minute detail:
100 / y (2 + 3) = 10 (original problem)
100 / y * (2 + 3) = 10 (for clarity, this does not change the problem)
100 / y * 5 = 10 (simplify the value in parenthesis)
(100 / y * 5) / 5 = (10) / 5 (divide both sides by 5)
100 / y = 2 (simplify)
(100 / y) * y = (2) * y (multiply both sides by y)
100 = 2y (simplify)
(100) / 2 = (2y) / 2 (divide both sides by 2)
50 = y (simplify)
y = 50

and there you have it.

well, that is not really formal, as i did not state the theorems required at each step. ive done these proofs a hundred times formally, which means you have to state things like, using the distributive property of multiplication, or using the reflexive property. but for the common man, i think this would pass as "formal" (even though my math instructors would give it a 2/10, if i was lucky).

9/19/2012 12:22 AM (edited)

caesari

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Say "Aye" if you're a nerd!!!

AYE!

9/19/2012 12:21 AM

darnoc29099

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Posted by coach_billyg on 9/19/2012 12:22:00 AM (view original):
Posted by darnoc29099 on 9/19/2012 12:13:00 AM (view original):
Apples and oranges are being discussed here. You don't use PEMDAS when solving for a variable, like the 100 / y(2+3) = 10 example. That's an equation where you need to isolate the variable, Y. All the math has already been laid out, and the answer is 2.

6 / 2(1+2) is an order of operations problem, where the PEMDAS acronym would apply (which says in order from left to right, you simplify Parentheses, Exponents, Multiplication and Division (simultaneously, starting from the left), then Addition and Subtraction (again, simultaneously)). This becomes 6 / 2 *3...3*3 = 9.
you are absolutely and completely wrong (no offense). you DO use pemdas to isolate for y, and i have no idea where the notion comes from that you would not. if you didn't, it would make no sense. for example, if you plug 2 into the original equation to see if it equals 10, you would obviously use pemdas, so you would get

100 / y (2+3) = ?
100 / 2 (2 + 3) = ? (substitution, y = 2)
100 / 2 * 5 = ? (do the parenthesis first
50 * 5 = ? (left to right)
250 = ?

you are supposed to get 10, this obviously does not work. pemdas always applies in these kinds of math problems. having variables or not has *absolutely* nothing to do with it.

if you want to isolate Y, here is how you do it. ill do it formally so you can follow every exact step in minute detail:
100 / y (2 + 3) = 10 (original problem)
100 / y * (2 + 3) = 10 (for clarity, this does not change the problem)
100 / y * 5 = 10 (simplify the value in parenthesis)
(100 / y * 5) / 5 = (10) / 5 (divide both sides by 5)
100 / y = 2 (simplify)
(100 / y) * y = (2) * y (multiply both sides by y)
100 = 2y (simplify)
(100) / 2 = (2y) / 2 (divide both sides by 2)
50 = y (simplify)
y = 50

and there you have it.

well, that is not really formal, as i did not state the theorems required at each step. ive done these proofs a hundred times formally, which means you have to state things like, using the distributive property of multiplication, or using the reflexive property. but for the common man, i think this would pass as "formal" (even though my math instructors would give it a 2/10, if i was lucky).

No offense taken, coach. The problem is we disagree on how the equation is written. You simplify your third line of work (100 / y *5) differently than I do (and probably anyone else who got y = 2). You're saying you think it's (100/y) *5. I believe it's 100/5y, with 5y all in the denominator. When you type the original left side of the equation (the way it was originally written) into Excel and plug in 2 for y, it returns 10. But I agree with your logic IF the equation was meant to be (100/y)*5.

9/19/2012 12:36 AM

isack24

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billy, just sent you a totally unrelated sitemail.

9/19/2012 12:42 AM

coach_billyg

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i see what you mean, darnoc. the TECHNICALLY correct way of reading that is unambiguous, when you put x (y), that is defined as X * Y. and if you want to divide by an expression, not a simple value or variable, there is no ambiguity in how you must do it - you must use parens on a single line to denote the expression, or you must place it on two lines with a large dividing horizontal line.

however, i can see how colloquially one could intend the entire part after the / to be the denominator, and write it that way.

really my major objection with your statement is that PEMDAS does not apply. and, it most certainly does.

and i think excel is pretty messed up with formatting. if you toss something like that in google, say 10 / 5 (1 + 1), it returns 4, not 1, which is technically correct. but i can see how a person could incorrectly write that expression and really mean
10
-----
5 (1 + 1)

if you think about fractions (which are simply division really, its funny to me that kids are taught about "fractions" when no such concept is really required. i think we were taught about fractions before division, which makes no damn sense, if you ask me. learn division first, and you can teach fractions in about 5 minutes), the way you are reading things to come up with 2 is very confusing. think about something like 1/3 (1/4). that definitely means a third times a fourth, but the way you are interpreting it would be 1 / (3 * 1/4) which is obviously totally different.

and just to be clear, because im not sure i was - there is absolutely no ambiguity in the math world, the way you and excel are reading the equation is incorrect. however, even knowing that, i can see why one might read it that anyway, if one were to guess the person who wrote the problem intended it differently than written. (these last two thirds of this post is really meant for the OP because im guessing that has something to do with why he started the thread).

9/19/2012 2:30 AM (edited)

dahsdebater

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This all seems like a little bit of a silly discussion given that in any remotely practical application it's probably safe to assume that the person solving the equation would know what it's actually supposed to look like/mean.

9/19/2012 1:06 AM

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