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If a bat and ball cost \$1.10, and the bat costs \$1 more than the ball, how much does the ball cost? (disregarding tax)

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The ball is 5 cents and the bat is \$1.05.

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Yes and here is proof:
bat + ball = \$1.10
bat = ball + \$1 (bat is a dollar more than ball)
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bat = \$1.10 - ball
ball = bat - \$1
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put bat from first eq. into second you get
ball = \$1.10 - ball - \$1
2 ball = \$0.1
ball = \$0.05 eg. 5 cents
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So the \$1.10 is without tax? Then wouldn't the answer be 10 cents? The bat costs \$1.00 and the ball costs 10 cents.

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I'll give you some extra time to noodle on this in order to see if anyone else gets the correct answer.
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Kay! :D
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No, the ball wouldn't be 10 cents. Because the bat is \$1 MORE than the ball. If I have 5 cookies, and you have 3 more than me, then that means you have eight cookies. We're adding onto the original 10 cents if that's the answer. If that was the answer, I got it!
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If it was the answer, then it would be \$1.10 + 10 cents.
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She said the bat and the ball cost \$1.10. If the bat costs one dollar more than the ball, how much is the ball? The ball alone didn't cost \$1.10. Both the bat and the call did.
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*ball.
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Okay, listen again. The bat costs \$1 more than the ball. That doesn't mean that the bat is \$1. It means that whatever the ball is, you take that value and add \$1 to it. If the ball is 10 cents, then you add a dollar to it.

Just like if I tell you that I have 3 more cookies than you do and you have 5 cookies. Does that mean that I have 3 cookies? No, I take your total amount of cookies and add 3 more to it.

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Let me add more to that.

"If the ball is 10 cents, then you add a dollar to it." When you add a dollar to it, then you have the cost of the bat itself.
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Wow even I got stumped on that one for a second Cal... And I'm a math nerd :/
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@amin: I think it's a psychological thing of some sort. When you first start, you think it's so simple, and so you automatically think the answer is that the ball is 10 cents. But if that's the case, then the total would end up being \$1.20. At one point, I thought there was no answer.
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The bat and the ball ALTOGETHER cost \$1.10. So, if the bat costs a dollar more than the ball, what do you get? The bat is \$1.00 and the ball is 10 cents.
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Then, what you're saying is that the bat is 90 cents more than the ball. AGAIN, the bat is \$1 more dollar than the ball. That means that whatever the bat is, it must be \$1 + B (the cost of the ball). If the ball itself is 10 cents, then that means that the bat (\$1 + b) is \$1.10. Therefore, if the bat is \$1.10 and the ball is 10 cents, then that makes the total altogether \$1.20.

Look at the equation I provided:(B is for the cost of the ball and T is for the cost of the bat.)

T = \$1 + B

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It could be psychological indeed, Passage.

40, by saying that the bat is \$1 and the ball is 10c, that's a difference of 90c, not \$1.

If you subtract \$1.05 and \$0.05, you get \$1, which is what the problem states.
If you add \$1.05 and \$0.05, you get \$1.10, which is what the problem states.
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OOOOOHHHHH. Amin just cleared it up with elementary problems. I hate math. Sorry for my argumentativeness and my stubborness. I hate math. Never really good at it.
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Yes. KitKat, Passage, and Amin got it right. And Amin is right that this has a psychological component.

I am currently reading a book entitled "Thinking Fast and Slow" by Daniel Kahneman, Professor of Psychology Emeritus at Princeton University, which deals with the issue how our brains function as two, somewhat collaborative entities which the author refers to as System 1 and System 2. The former is responsible for automatic and ceaseless responses based on inferences which are often very superficial (the ball is \$0.10), and System 2 is the logical portion which is supposed to analyze and evaluate System 1's automatic responses and over-ride them when necessary (like refraining from blurting out in a crowded restaurant that someone is ugly). However, as the author explains, System 2 is lazy and doesn't always do a very good job (although given enough time, it will eventually determine that the ball is \$0.05 if properly motivated).

The reason evolution has made System 1 the way it is is so we can make at least some semblance of an appropriate response when time is of the essence. Otherwise, about 100,000 years ago, sabre tooth tigers would have simply walked up and eaten all of us as we tried to reason through all the possible actions to take in order to decide which one is best. All this, of course, is an over simplification of the results based on the author's copious amounts of research over the last 40 years.

This puzzle was used in a research study where 50% of students from MIT, Princeton, and Harvard gave the wrong answer. And the percentage was probably only that good because it would have been obvious to some that a question which seems so simple on the surface probably has more to it. This why when something looks so simple and obvious to us, that means it is worthy of a second look.
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I'm confused all over again. I suddenly don't see how five cents is the answer. But given the fact that three people got this answer right, according to you, I am most likely wrong. So I'm just gonna be wrong and stop arguing over something I can't explain.
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@Cal: Wow. You know, that's actually saying something because I know students from MIT, Princeton, and Harvard tend to be the highest educated. On the other hand, it could also be one of those context things. Whether or not we can provide the correct answer depends on the context rather than the problem itself.

It's like having cards and saying "If I have an even number on one side, then there will be a vowel on the other" and then you ask what cards must be turned over to disprove or argue the rule. Most people who did that could not get it right.

However, when it came to a social context, most people did get it right. They were asked instead "Only a person 21 or older can drink an alcoholic beverage" at a party and given 2 ages and 2 drinks. They were asked which ones would argue or disprove the rule.
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Fascinating discourse, Cal. I'm assuming that when trained properly, System 2 elevates one's intellect?
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@dawg: Ok, let's say the ball is x and the bat is 1+x since it is \$1 more than the ball. Therefore, 1 + x + x = 1.10
Here is the formula :
1 + x + x = 1.10
1 + 2x = 1.10
2x = 1.10 - 1
2x = 0.10
x = 0.10 / 2
x = 0.05

I hope that clears it up for you.
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Then, all you have to do is replace both x's with \$0.05 and you get 1 + 0.05 + 0.05 = 1.10 so the bat costs \$1.05 and the ball costs \$0.05
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