How much do you understand this math question?

[Cutesie]

It's not one nor the other, but rather both answers are correct.
Bat ($1.00) + ball ($0.10) = $1.10 with the bat being $1.00 more than the ball. Correct.
Bat ($1.05) + ball ($0.05) = $1.10 with the bat being $1.00 more than the ball. Correct.

Nope. Your first scenario has the bat costing 90 cents more than the ball.

100 - 10 = 90

 

[Cutesie]

If no one minds, let's switch to whole numbers and nit specify a currency:

If a bat and ball cost 110 in total, and the bat is 100 more than the ball, how much would the ball cost?

Does that make it easier?

 

[Misty Avich]

It's not one nor the other, but rather both answers are correct.
Bat ($1.00) + ball ($0.10) = $1.10 with the bat being $1.00 more than the ball. Correct.
Bat ($1.05) + ball ($0.05) = $1.10 with the bat being $1.00 more than the ball. Correct.

Apparently the answers are supposed to depend on thinking style or something, where more logical, analytic thinkers may see the latter as the correct answer, while the former is more like a bigger picture thinker. I don't have that autism logic.

 

[Misty Avich]

It makes sense in money speaking. Say if you saw two items in a store, one costing £20, one costing £25, you'd go "oh the second item is £5 more than the first".

 

[Cutesie]

That's not the equation, though. It's 1.00 + 0.10 = 1.10,...or 1.10 - 1.00 = 0.10.

We have two requirements:

1) A total of 1.10
2) The bat costing 1.00 more than the ball

If the ball is 0.10 and the bat is 1.00, condition #2 is not fulfilled. The difference is 90 cents, not a dollar.

 

[Hypnalis]

Cutsie is correct.

There's one solution that satisfies both conditions.: ball 0.05, bat 1.05

There are an infinite number of solutions to "bat + ball = 1.10"
There are 109 integer solutions "bat + ball = 1.10" with non-zero prices.

Two simultaneous equations with two variables (and two distinct conditions set in the equations) have only one solution. (**)

This can be easily proven.


(**) e.g. the same equation stated twice is a different case

 

[717]

If a bat and ball cost $1.10 in total, and the bat is $1 more than the ball, how much would the ball cost?

The answer should be 10 cents but apparently it's not, and according to this article autistic people are supposed to understand that the answer is 5 cents. I've re-read the question and also this article but I still don't get it. 10 plus 100 is always 110, isn't it? Or do dollars and cents have a different rule?

MSN

The bat cost 1 more than the ball.

If you say the ball cost 0.10 that means the bat should cost 1.10... meaning 1 more than the ball. But the total is already 1.10 for both, so the ball cant be 0.10

If you say the ball is 0.05 then the bat is 1 more than that, and this is 1.05, in this case the total is 1.10

 

[Crossbreed]

So we use a 5, meaning the ball cost 5p and the bat cost...£1.05?

Yes.

 

[Misty Avich]

Actually, wouldn't it be the other way around? I mean, NTs are supposed to be able to read between the lines, so shouldn't they be the ones who should come up with the other answer?

What is the difference between reading between the lines and noticing details?

 

[Cutesie]

Actually, wouldn't it be the other way around? I mean, NTs are supposed to be able to read between the lines, so shouldn't they be the ones who should come up with the other answer?

What is the difference between reading between the lines and noticing details?

Reading between the lines means seeing the big picture. One can look at something and see what isn't explicit. In the case of written material, an autistic person is more likely to only understand the exact words used. They'll miss out on things such as the nuance of tone and what the author chose to leave out.

Noticing details can sometimes be close to the opposite. One can hyper-focus on the nitty-gritty details and lose out on the general idea that's trying to be conveyed.

 

[Crossbreed]

What is the difference between reading between the lines and noticing details?

Those with a "bias" are happy if they only satisfy one of the requirements.
When you notice details, you notice that the second requirement was not met.

Algebra just gives a methodical process for satisfying both.

 

[Misty Avich]

So a big picture thinker would immediately miss the word "more" in the math problem here and just answer it as 10.

 

[Cutesie]

I'm sorry. My previous comment was not written very well, and it only took the negatives of autism into account. Being detail-oriented could be a great asset.

 

[UFO]

So a big picture thinker would immediately miss the word "more" in the math problem here and just answer it as 10.

Only if they haven't learned to think differently.

I heard this math problem more than decade ago. My first thought back then was $0.10, just like everyone elses, but I also realized immediately that it can't be the answer because someone had decided that this problem was worth of publishing. Who would publish in math problem article a problem with an obvious solution?

That was a matter of experience, not a matter of autism or different way of thinking. I have learned but not born with the understanding that this kind of questions are tricky.

Being able to approach the problem in a mathematical way ("bat = $1 + ball", "bat + ball = $1.10", substitute "bat" and end up "($1 + ball) + ball = $1.10", solve "ball") is also something that must be learned. I don't think that anyone can be born with an understanding of algebra and arithmetic. (Thought one can realize on his/hers own, that every individual finger can be used to represent one individual item of a group they want to count.)

Reading between the lines means seeing the big picture. One can look at something and see what isn't explicit.

I just love to tell one anecdote from my childhood (and ask do you guys have similar experiences of "not being able to connect dots"?):

I am good at math. I have been called "mathematically talented". I dislike math, but I seem to get it quickly. In elementary school we were taught division and fractional numbers. I got good grades from math exams. And boy I got laughed at by even the thickest non-mathematical minds of the class when they realized that I couldn't answer immediately to a question "is 3 divided by 4 same as 3 parts of 4?" I just never thought that they are same mathematical operation despite me being able to quickly end up with the correct decimal numeric answer.

I still don't understand how I managed to avoid making such conclusion. I don't even remember how I exactly calculated those back then, I probably used some kind of iterative adding and subtracting method so I never had to think that I was actually dividing things.

One of those little pieces of evidence that I might be neurodivergent...

Those with a "bias" are happy if they only satisfy one of the requirements.

That is exactly how I have understood that the stereotypical autistic thinking works:

Stereotypical neuronormals naturally try to find quick and dirty model that fits to currently perceived situation. They abandon that model only if details start to contradict it too much.

Stereotypical autistics naturally just observe details until they can figure out a model that matches perfectly the currently perceived situation. Their brains can't accept contradictions.

 

[Misty Avich]

I guess even people who are good at math can still make a mistake or not get a math problem. A bit like me with spelling, I'm excellent at spelling but sometimes I come across a word that I don't know how to spell.

 

[Crossbreed]

I guess even people who are good at math can still make a mistake or not get a math problem. A bit like me with spelling, I'm excellent at spelling but sometimes I come across a word that I don't know how to spell.

Some math (& physics) problems do not work like we intuitively expect them to, but solid math shows us why.

 

[Forest Cat]

I just want to know where you can buy a bat for 1 dollar. Mine cost 60 dollars. Can't buy a bat for 1 dollar, or a ball for 10 cents, I say all this is completely wrong. It's a trick question.

 

[UFO]

I just want to know where you can buy a bat for 1 dollar

Can't buy a bat for 1 dollar, or a ball for 10 cents, I say all this is completely wrong.

I don't know how much pet stores charge for bats. I also fail to understand how they ended up with so unrelated things as animals and dance events. But that is not the point of the math problem.

 

[Cutesie]

1 + 0.1 = 1.1 The condition is fulfilled. Where are you coming up with 0.9? The total is 1.1, not 1.

1 + 0.1 = 1.1 fulfills condition #1. It does not fulfill condition #2 - that one has to be 1.0 more than the other.

I'm getting off now at least until tomorrow night.

 

[TBRS1]

Has anybody noticed that this is much less a math problem, and much more a language problem, in which people fail to apply the literal meaning of the phrase "more than"?

As I mentioned, this is a standard question in certain types of research. It has been asked of math majors in universities. They answer correctly only slightly more often than average.