What's stopping me from just, y'know, taking the book and running?
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A book costs $1 plus half its price. How much does it cost?
- Thread starter donphan fan
- Start date
it would actually approach a value below 2 that could be defined by some term of the constant e but what exactly that is i have no idea (i'm not a math major donphan fan
this question drove me to a life of crime, thank u smogoff
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GUYS
I WILL SOLVE THIS PHILISOPHICAL QUESTION
*eats the book*
I WILL SOLVE THIS PHILISOPHICAL QUESTION
*eats the book*
damn, most people here were so sure that it was $2...
but donphan fan was brave enough to stand up and give us an alternative account.
but donphan fan was brave enough to stand up and give us an alternative account.
0$ cause I'm cheap and I'd actually just read it at the store like a nerd. (I do this a lot)
As a pure math problem, with p = price:
$1 + p/2 = p
$1 + p/2 - p/2 = p - p/2
$1 = p/2
p/2 = $1
p = $2
As a question about sales and it being one dollar more than half price: That requires information not given, so it's unanswerable.
1/3 = 0.3333...
2/3 = 0.6666...
3/3 = 0.9999...
But 3/3 = 1/1 = 1, so 3/3 = 1 and 3/3 = 0.9999...
Thus, 0.9999... = 1
The basic algebra and the infinite sum are interchangeable. Frankly, computing it as an infinite sum is a waste of knowledge of infinity.
$1 + p/2 = p
$1 + p/2 - p/2 = p - p/2
$1 = p/2
p/2 = $1
p = $2
As a question about sales and it being one dollar more than half price: That requires information not given, so it's unanswerable.
Not quite how infinite values (or 1/value) works.
1/3 = 0.3333...
2/3 = 0.6666...
3/3 = 0.9999...
But 3/3 = 1/1 = 1, so 3/3 = 1 and 3/3 = 0.9999...
Thus, 0.9999... = 1
The basic algebra and the infinite sum are interchangeable. Frankly, computing it as an infinite sum is a waste of knowledge of infinity.
it's not ironic. this is real math done by real people (me)
I don't get how it would approach 2 cuz 1 +.50 is 1.50, half of 1.50 is .75 and .75+1.50 =2.25.
1,333333333 + 0,66666666 = 2 (or very close to 2)
Guys…I ate the book…
How did it taste?
Yeah but how are u getting. 66 and 1.33?
it approaches 2 if you apply "a dollar plus half its price" on every iteration. so you have 1 + 0.5 = 1.5, 1 + 0.75 = 1.75, 1 + 0.875 = 1.875, 1 + 0.9375, etc etc.; just eyeballing it you can see the equation progresses as 2 - 1/2, 2 - 1/4, 2 - 1/8, 2 - 1/16, and so on until the fraction approaches zero and thus the sum approaches 2. solving it algebraically (assuming price and cost mean the same in this context) also gives x = 2 as solved early in the thread.
the price is a constant 1$ plus half of its final price. You're adding the new iteration to the initial cost of 1$, not the value you had just solved for.
Here's a third way to think of it. The price of the book (x) can be put into the formula x=1+1/2(x).
Simplify this down to x=1+x/2
Then turn 1 into 2/2 and simplify to x=(2+x)/2
From there the equation can be simplified to 2x=x+2
Subtract x from both sides to get x=2
It's a bit drawn out but it should explain the much simpler method compared to my geometric sequence method earlier and Tea Guzzler's non-algebraic method.
The book is $1 half of 1 is 0.50. 1+0.50=1.50.
I mean either way that's really cheap for a book so I'm not complaining.
The best way to word the problem would be "the price of the book is 1$ plus half of its final price" but the general consensus is that it's equal to 2. Not sure who voted 1.5 ngl
ok but now the price of the book is 1.50. half of 1.50 is 0.75. 1+0.75 is 1.75. rinse and repeat until you get 2.
Me, I did