Maths question

Maths question

Q: If a baseball and bat cost $110, and the bat costs $100 more than the ball, how much does the ball cost?

$101! (hint: not decimal)

Amusing. Reminds me of the wee tests like this once got in Primary School. Enjoyable though.

Except that in primary school we had to deal with decimals in such cases.

B = ball
T = bat
___________
T + B = 110
T = B + 100
-----------------
B + 100 + B = 110 => 2B = 110 - 100 => 2B = 10 => B = 10 : 2

The ball would cost $1.98 at the local Walmart where I shop. Their bats are only $6.95.

Where in hell are you folks shopping?

It's obvious from the starting post. 'Twas America dear blind one, 'twas America. Ha, ha.

I use this equation:

b+t=110

t=100+b

And I use Wolfram|Alpha to do the solving.

And yes, I am the type of guy that use equations. Explanation:

The ball and the bat cost $110. Therefore, if we let ball = b and bat = t we get the equation
b + t=110

Also, the bat costs $100 more than the ball. That means the cost of the bat is (100+b).

Then we substitute the bat equation t into the original equation and we get
b+ (100+b) =110

Using a graphic calculator, you then solve for b:
Syntax for a TI calculator:
solve (b+ (100+b) =110), b

Originally posted by Krake:

Except that in primary school we had to deal with decimals in such cases.

B = ball
T = bat
___________
T + B = 110
T = B + 100
-----------------
B + 100 + B = 110 => 2B = 110 - 100 => 2B = 10 => B = 10 : 2

Or you could just use a graphic calculator

Originally posted by wikipedian:

Or you could just use a graphic calculator

It probably takes less time to do it in your head than to type it in or write it down. Btw, are you familiar with this story? http://www.themathlab.com/writings/short%20stories/feeling.htm

I side with Jaybro on this one. That must be some bat if it costs $100.00, I can't think of any sporting goods store that would dare try to get that price for a bat and ball.

Eh, I figure it's much harder to be misled by realistic values. This question is designed specifically to look really easy and thus to lead you astray with a seemingly super easy and obvious answer.

I found the math sooooo difficult!

That would be five, wouldn't it?

Oh!! I get it!!!

Originally posted by johnnysaucepn:

Q: If a baseball and bat cost $110, and the bat costs $100 more than the ball, how much does the ball cost?

I tried ticking all of the options, but it didn't work. Can somebody help me?

I know that the obvious answer to my question is, No! But please try. I'm begging you.🙏

Originally posted by mjmsprt40:

I side with Jaybro on this one. That must be some bat if it costs $100.00.

This one cost me $3.98. I call him Sleepy.

Originally posted by jbrothernew37:

Originally posted by johnnysaucepn:

Q: If a baseball and bat cost $110, and the bat costs $100 more than the ball, how much does the ball cost?

I tried ticking all of the options, but it didn't work. Can somebody help me?

I know that the obvious answer to my question is, No! But please try. I'm begging you.🙏

See my explanation above. The ball costs $5 and the bat $105.

Originally posted by jbrothernew37:

I found the math sooooo difficult!

Use a calculator or paper and pencil.

Scrap the calculators and just use your noggin. The bat and ball combined are 110, the bat costs 100 more than the ball, the ball costs 10.

Then, laugh yourself silly as you walk out of the store and decide to shop at a place that has more reasonable prices. Unless you're really into gold-plated bats and fur-lined baseballs. To each his own.

In that the bat is only $90 more.

the ball is $5

Originally posted by mjmsprt40:

Scrap the calculators and just use your noggin. The bat and ball combined are 110, the bat costs 100 more than the ball, the ball costs 10.

My calculator and equation says otherwise. The ball costs $5 and the bat $105. 5+105 = $110.

_____________________________________________________________________________________

Just found out your error. You have to plus the two objects together to equal $110. If the ball costs $10 and the bat is $100 more expensive, its cost is $110. However, if you add $10 and $110 ($10+$110), you get $120 and not $110.

Originally posted by wikipedian:

My calculator and equation says otherwise. The ball costs $5 and the bat $105. 5+105 = $110.

Just found out your error. You have to plus the two objects together to equal $110. If the ball costs $10 and the bat is $100 more expensive, its cost is $110. However, if you add $10 and $110 ($10+$110), you get $120 and not $110.

If we're being wordy

101 = 2^0 + 0*2^1 + 2^2 = 1 + 4 = 5

Interesting results here.

Of course, if I were to give the game away, I would have had the poll include options for whether the responder was religious or not.

http://www.sync-blog.com/sync/2012/04/simple-math-problem-could-indicate-your-religious-beliefs.html

This is all just for fun, and not the be considered scientific evidence. But it's interesting...

My initial reaction was in fact $10, but then I read it a second time and realized it said the baseball and bat cost $110 together, and that it wouldn't make sense to say $10 because 10+110 would be 120.

Interestingly, here's someone who applied sufficient thought to the original question but not to the explanation given by one commenter: http://www.sync-blog.com/sync/2012/04/simple-math-problem-could-indicate-your-religious-beliefs.html/comment-page-1#comment-78861

I answered $37.54 and am a Buddhist from Tuscaloosa, Alabama.

Any questions?

I answered $37.54 and am a Buddhist from Tuscaloosa, Alabama.

Any questions?
.....

If that was your answer, you are an analytical thinker and – according to results of this study – more likely not to have any religious beliefs. If you said the ball cost $10 (and I confess to being one of those people), you are an intuitive thinker and thus more likely to hold a religious belief of some kind.

My guess is that people are most likely to be religious or not based on whether or not their parents were, and not on the cost of a hockey stick.

Psychologists!
.....
From somewhere.

At this point it must be clear to the intelligent reader that clinical psychology can make virtually any claim and offer any kind of therapy, because there is no practical likelihood of refutation – no clear criteria to invalidate a claim. This, in turn, is because human psychology is not a science, it is very largely a belief system similar to religion.
.....
In the same way that everyone is a sinner in religion's metaphysical playground, everyone is mentally ill in psychology's long, dark hallway – no one is truly “normal.” This means everyone needs psychological treatment. This means psychologists and psychiatrists are guaranteed lifetime employment, although that must surely be a coincidence rather than a dark motive.

Does that mean there are no religious mathematicians? Cause in math there is only right answer, so as in life. $10 and $110 is wrong since the final total will arrive at $120 and not $110. You can't have a $10 ball and a $110 bat and get the total at $110. Therefore, the answer must be $5 ball and $105 bat.

The question is worded to deceive you. The assumption would seem to be religious people are less likely to look past their original conclusions and analyze meaning based on the writer's intentions or actual meaning.

Originally posted by wikipedian:

Does that mean there are no religious mathematicians? Cause in math there is only right answer, so as in life. $10 and $110 is wrong since the final total will arrive at $120 and not $110. You can't have a $10 ball and a $110 bat and get the total at $110. Therefore, the answer must be $5 ball and $105 bat.

I don't think mathematicians typically work all that much with linguistic trickery. What you say isn't true anyway. If you have a series like 1, 2, 3, 4, 5 and the question is how it continues you could go for the obvious f(x)= x + , if x = ℤ, or you could devise all kinds of functions that just happen to pass by those numbers.

Originally posted by ensbb3:

The question is worded to deceive you. The assumption would seem to be religious people are less likely to look past their original conclusions and analyze meaning based on the writer's intentions or actual meaning.

Yeah, it's just not the kind of problem you'll ever be faced with in a store. Now if it were a question about how to compare the price of flour given in kg by one brand and in L by another… that's something you actually encounter. So you could say Brand A costs €1/L, while Brand B costs €.80/kg. Brand A is LxWxHmm while Brand B is LxWxHmm. Which one's actually cheaper under the assumption that both flours occupy the same volume? I have never bothered to work that one out, but my point is that you might actually come across it in real life. You're never going to be in a store and know that the bat is $100 more than the ball without knowing the actual price of either. Basically you're reasoning backwards here. You'd know the ball is $5 and the bat $105. Based on that you'd say the bat is $100 more.

I know this is off topic, but I can't help myself.

Wikipedian:
"Character is a journey, not a destination"--Bill Clinton

I did not have sexual relations with that woman, Miss Lewinsky.

Originally posted by jbrothernew37:

I know this is off topic, but I can't help myself.

Wikipedian:
"Character is a journey, not a destination"--Bill Clinton

I did not have sexual relations with that woman, Miss Lewinsky.

And? Bill made some bad choices. Doesn't anybody? Plus, I like that quote about character building.

Originally posted by ensbb3:

The question is worded to deceive you. The assumption would seem to be religious people are less likely to look past their original conclusions and analyze meaning based on the writer's intentions or actual meaning.

There is absolutely no deception in the question. There is no excessive wording put in place in order to obfuscate the question, there's no call to treat this as a real hypothetical shopping situation. This isn't a shaggy-dog story, it's on the same level of primary school arithmetic questions. The question is clear, what matters is that most, if not all, people naturally leap to an intuitive answer that is wrong. But some take the time to check their results and reason the correct answer, whereas some people prefer to stick to their intuition. And remain wrong.

I made the point in another thread that people are notoriously poor at estimating long-term risk. This is partly the reason why. The human brain is tuned to making broad estimates quickly, even when those estimates are factually wrong.

Imagine you're driving a bus. At the first stop, 7 people get on. At the next, 4 people get on and 3 get off. At the next stop, another 4 get on, but nobody gets off, while further on, 2 get off and nobody gets on. At each of the three next stops, 2 people get off, except for the last, where 3 get off. The next stop is the end of the line, and everyone left on the bus gets off. What is the driver's name?

Now that's a deceptive question.

Originally posted by johnnysaucepn:

There is absolutely no deception in the question. There is no excessive wording put in place in order to obfuscate the question, there's no call to treat this as a real hypothetical shopping situation.

I have to disagree with you there. It's talking about real goods and Dollar values. A non-deceptive question would be something like: x and y add up to 110. y is 100 more than x. Solve for x.

Originally posted by johnnysaucepn:

Imagine you're driving a bus. At the first stop, 7 people get on. At the next, 4 people get on and 3 get off. At the next stop, another 4 get on, but nobody gets off, while further on, 2 get off and nobody gets on. At each of the three next stops, 2 people get off, except for the last, where 3 get off. The next stop is the end of the line, and everyone left on the bus gets off. What is the driver's name?

Now that's a deceptive question.

Degrees.

Originally posted by Frenzie:

I have to disagree with you there. It's talking about real goods and Dollar values. A non-deceptive question would be something like: x and y add up to 110. y is 100 more than x. Solve for x.

How does dollar values make the question deceptive? If anything, presenting it in mathematical terms makes the question more deliberately confusing and off-putting.

If you ask a five-year-old, "If you have ten apples, and someone gives you ten apples, what do you have?", the answer being sought is not "a basketful".

"Solve for x" is not something that lends itself to an intuitive answer, which is the aim of the question.

Originally posted by johnnysaucepn:

"Solve for x" is not something that lends itself to an intuitive answer, which is the aim of the question.

And thus it is deceptive. QED.

Pointless anyway. I don't think they sell baseball and bat sets for $110.00, even on Michigan Avenue where everything has an ungodly price. If you did pay that much, I can't imagine you using it to actually play a game.

Oh, man, think what the catcher's mitt would have to cost. You could probably buy a catcher for less.

Originally posted by Frenzie:

Originally posted by johnnysaucepn:

"Solve for x" is not something that lends itself to an intuitive answer, which is the aim of the question.

And thus it is deceptive. QED.

So, you're saying it should be confusing and obscured in order to not be deceptive?

I would have loved to use that in an exam. "Sir, I know I answered 3, while you claim the answer to be 4, but I believe the question is deceptive because I came up with the wrong answer."

A classical:
A pilgrim was on his way to Mecca. Arriving to a fork he didn't no which direction to go. Close by was a tavern he already heared about. The tavern was famous for the two men working there. One always said the truth whereas the other always lied. Our pilgrim entered the tavern and asked one of them a single question. He didn't know if he speaks to the liar or the one that always tells the truth. However he was very satisfied with the answer since he knew now which direction to go.
What was his question?

Anybody for solving the puzzle with the help of math? It is math at primary school level. No calculators needed.

Originally posted by johnnysaucepn:

So, you're saying it should be confusing and obscured in order to not be deceptive?

If you insist on calling it "confusing and obscured," sure. That way you know exactly what's being asked, while in your question you're using objects from real life in a situation in which they'd never occur. The deception lies in needing to realize that the question asked has in fact little relation to reality but is a simple algebra question. Phrasing the question in "confusing and obscured" mathematics immediately makes it clear what kind of problem you're dealing with. It's no different than poetry versus prose. You can call poetry "confusing and obscured," but you immediately engage it in the right frame of mind when you see it. In any case the mathematics I wrote shouldn't be confusing to anyone over the age of 14 or so, unless I used incorrect English terminology as I really only know math in Dutch. So fine, it'd be less obscured by the English language if rephrased as follows: x + y = 110; y = 100 + x; x = ?.

I would have loved to use that in an exam. "Sir, I know I answered 3, while you claim the answer to be 4, but I believe the question is deceptive because I came up with the wrong answer."

What does that have to do with anything? Unless you're referring back to what I said to wikipedian that doesn't in any way derive from what I said. I didn't say it's bad that the question is deceptive, but if there's an intuitive answer that requires further examination then I simply don't see how you can claim it's not a deceptive question.

Originally posted by Krake:

Anybody for solving the puzzle with the help of math? It is math at primary school level. No calculators needed.

What kind of math are you thinking of? You just ask 'em what the other would say and do the opposite.

Originally posted by Frenzie:

The deception lies in needing to realize that the question asked has in fact little relation to reality but is a simple algebra question.

Algebra is a means of abstracting elements of a question away from reality. It's no less valid whether you use X or dollars. Newton's laws of gravitation apply to real objects as well as abstract ones, otherwise they wouldn't be any use at all.

In what way does the question not have relation to reality? The only objection to the question seems to be that no-one knows what store would sell a baseball and bat for $100 dollars. The question is, "how much does the ball cost?", not "can you find me this shop?" You have to accept the axioms of the question - it matters not one iota whether it's actually likely to happen in reality. There is no information withheld, no information obscured. You should know as well as I do that X is just a label, and may as well be 'baseball bat'.

To use my earlier example: if I asked a little kid, "If you had five apples, and I gave you five, how many apples do you have?", I wouldn't expect any of the following answers to be considered correct:
"Where did the first five apples come from?"
"Why would you want to give me five apples?"
"Why would I want nine apples anyway?"
"None, because I don't have any apples, and you don't have any either"

Originally posted by Frenzie:

What kind of math are you thinking of? You just ask 'em what the other would say and do the opposite.

The algebraic form of the solution you gave.

Truth = +1
Lie = -1
-----------------
(+1) x (-1) = -1
(-1) x (-1) = +1

Originally posted by Krake:

Originally posted by Frenzie:

What kind of math are you thinking of? You just ask 'em what the other would say and do the opposite.

The algebraic form of the solution you gave.

Truth = +1
Lie = -1
-----------------
(+1) x (-1) = -1
(-1) x (-1) = +1

Hmm, not sure it's actually possible to multiply the truth.

Originally posted by johnnysaucepn:

In what way does the question not have relation to reality?

I already said: you're reasoning backwards from what you'd do in real life.

The only objection to the question seems to be that no-one knows what store would sell a baseball and bat for $100 dollars.

I'm not objecting to the question. I'm objecting to your claim that it's not deceptive — much like how in the other thread I object to calling packaging with icky pictures on it plain packaging. I suppose you could say I'm definition trolling.

The question is, "how much does the ball cost?", not "can you find me this shop?" You have to accept the axioms of the question - it matters not one iota whether it's actually likely to happen in reality. There is no information withheld, no information obscured. You should know as well as I do that X is just a label, and may as well be 'baseball bat'.

You must have missed what I wrote above. And you know as well as I do that our brains play tricks on us, whether they're auditory, visual, linguistic or mathematical illusions.

Originally posted by johnnysaucepn:

To use my earlier example: if I asked a little kid, "If you had five apples, and I gave you five, how many apples do you have?", I wouldn't expect any of the following answers to be considered correct:"Where did the first five apples come from?""Why would you want to give me five apples?""Why would I want nine apples anyway?""None, because I don't have any apples, and you don't have any either"

But that question is very much the same kind of calculation you actually do in stores while shopping for bats and balls, or for apples. It's not misguiding you by giving unnatural types of information.

This is another one of those "Johnny is right cause he wants to be" issues, huh?

The question is deceptive. It can be worded more clearly but is worded to give some the wrong impression. Not me, but then you wouldn't of posted it if the answer was outright obvious to everyone so I read it carefully.

Originally posted by ensbb3:

you wouldn't of posted it if the answer was outright obvious to everyone so I read it carefully.

Exactly, I'm not sure how this is even a point of contention. The effect is well-known — the site even lists the same example as a question specifically designed to lead to an intuitive answer.

Originally posted by ensbb3:

This is another one of those "Johnny is right cause he wants to be" issues, huh?

No, that just sounds like a "Johnny is wrong because I want him to be" sort of argument. I'm disappointed in you.

Originally posted by ensbb3:

The question is deceptive. It can be worded more clearly but is worded to give some the wrong impression. Not me, but then you wouldn't of posted it if the answer was outright obvious to everyone so I read it carefully.

Then tell me, like I've been asking all along. What is the wrong impression you're supposed to be getting? In what way does the phrasing of the question actually lead you to believe that $10 is the right answer, and that $5 is not?

Regardless of whether you think that phrasing a question in casual terms makes it more likely that you will jump to the wrong conclusion, the point is that that's your cognitive processing of the question - it's the way your brain falsely interprets it. There isn't anything wrong with the question - it's your brain that's being deceptive.

If it takes 2,500,0000 years for light from the Andromeda galaxy to reach us, how long would it take light from Rjhowie to reach us?

Show the math, please.

Originally posted by johnnysaucepn:

Originally posted by ensbb3:

This is another one of those "Johnny is right cause he wants to be" issues, huh?

I'm disappointed in you.

Originally posted by Johnny:

Originally posted by ensbb3:

The question is deceptive. It can be worded more clearly but is worded to give some the wrong impression. Not me, but then you wouldn't of posted it if the answer was outright obvious to everyone so I read it carefully.

Then tell me, like I've been asking all along. What is the wrong impression you're supposed to be getting? In what way does the phrasing of the question actually lead you to believe that $10 is the right answer, and that $5 is not

It's been tried. That you rejected the answer isn't my problem.

It's not how a question in reality would ever be worded. It isn't instantly clear because if you mention the combined price of two things the only other figure seemingly relevant would be the price of one of the items... To leave the math for one item to the person is standard and elementary. To make them figure the price for both items after you've already given them two prices is rude and nonstandard, therefore to some it's deceptive.

Whether or not it's deceptive to you, Johnny, is irrelevant. Some people are having trouble with it. Since that is a thing, and apparently from your link a common thing, I say it's deceptive even tho it didn't deceive me.

Originally posted by johnnysaucepn:

Regardless of whether you think that phrasing a question in casual terms makes it more likely that you will jump to the wrong conclusion, the point is that that's your cognitive processing of the question - it's the way your brain falsely interprets it. There isn't anything wrong with the question - it's your brain that's being deceptive.

1) It's well known that your brain can be deceived by certain things.
2) The question was designed to take advantage of this well-known fact.

According to you: 1,2 => The question is not deceptive.

Your argument seems to be of the same class as saying that deliberately holding back relevant information isn't lying because you need to actually tell untruths to deceive.

Originally posted by ensbb3:

Whether or not it's deceptive to you, Johnny, is irrelevant. Some people are having trouble with it. Since that is a thing, and apparently from your link a common thing, I say it's deceptive even tho it didn't deceive me.

Not even for a split second? I solved the entire thing pretty much subconsciously, but the part of the thought process that came through to me went something like "10… wait a second… that's not right… stupid brain… oh yeah, it's 5, 'cause 105+5=110. Now let's phrase it in binary."

Originally posted by ensbb3:

It's not how a question in reality would ever be worded.

But that is exactly the way that that question is being worded. In reality. This is not acting class - you're not being asked to consider motivation from the point of view of a person in a shop. It doesn't ask you whether that's something you're likely to need to know in your day-to-day life. It doesn't ask you whether you would personally want to ask another person that question.

The question is unambiguous. The language is clear. The question doesn't get any less deceitful by translating it into algebraic form.

When you sat exams, did the questions say, "A train leaves New York at 2pm, travelling at 70mph. A second train leaves New York at 4pm, travelling at 80mph. We were going to ask you what time they pass on the line, but we realise that this is not a question anyone's ever likely to ask you in reality, and it's terribly rude of us to ask you to work it out for yourself when we blatantly already know the answer, so let's just forget the whole thing"?

Originally posted by Frenzie:

1) It's well known that your brain can be deceived by certain things.
2) The question was designed to take advantage of this well-known fact.

Really? What certain things in the question are causing your brain to be deceived? What part of the question has been designed to trick you?

Originally posted by Frenzie:

According to you: 1,2 => The question is not deceptive.

Correct. Just because your brain makes a mistake, does not mean there is anything wrong with the question.

You didn't ask when trains will pass.

This wasn't declared to be an exam.

Next time someone asks you the price for somethings give it to them in the format above so they have to figure it all and see how helpful they think you are... in reality.