I’m sure you have heard of this math problem. No matter how many times someone explained this to me I still feel confused. Can someone explain in the simplest way possible?

In: Mathematics

What part of this you have problem with? Please provide more context.

The only constrains are that

1) bat price + ball price is $1.10, and

2) price of ball + 1$ = price of the bat.

So the only numbers that work with this is 0.05$ and 1.05$. Do you have problem with equation that should be written?

A bat and ball cost $1.10 in total. The bat costs $1 more than the ball. So you take the price of the ball and add the one dollar, to make the bat cost $1 more than the the cost of the ball So the ball costs $0.05 and the bat would cost $1.05.

This is an algebra problem.

Bat = x

ball = y

So lets convert the words to a math expression. price of both together is $1.10 which looks like:

x+y = 1.1

And then the bat is the price of the ball plus $1 which looks like this:

x = y+1

So we have two unknown values and two equations. If we put the second equation into the first then we can eliminate one variable and solve.

(y+1) + y = 1.1

2*y + 1 = 1.1

2*y = .1

y = .05

So the ball costs 5 cents. Now you can enter this number into either equation to find out how much the bat costs (it’s $1.05).

There’s a really interesting book called Thinking Fast and Slow that goes into why this problem catches so many of us out.

Kahneman proposes two systems of thinking, one which processes information very fast and comes up with intuitive answers, and one which is slower, more logical and can be used to “check” the other system.

The question itself has primed you into thinking it’s an easy or obvious answer , and a lot of people may not necessarily double check their working.

It’s a good illustration of the problem of relying on intuitive thinking alone – things can seem obvious and still be wrong. Not to say intuition has not been incredibly useful to humans as a species and is not to be relied on at all – as the Russians might say : trust, but verify.

Edit: just to add that your brain is taking in the problem as 1 x bat and 1 x ball and equivocating it with 1 x $1 and 1 x $0.10 . It then associates “bat” with $1 and basically blurts out the answer without thinking.

Interestingly, kahneman goes on to say in the book that when the problem was made to be more physically difficult to read, less people were caught out by it- suggesting that when you are required to concentrate the rational part of your brain kicks in. You should really read the book , it’s fascinating.

“A bat and a ball cost $1.10 in total. The bat is $1 more than the ball. How much is the ball?”

Your immediate thought may be that it’s $0.10. OK, let’s try that!

* Say that the ball is $0.10.

* Then the bat is $1.10 ($1 more than the ball).

* Now both of them combined would be $1.20.

Hrmm, that didn’t work. Why not? Well, the problem kinda “tricked” you – as soon as you heard “$1.10” and “$1 more”, you immediately jumped to “$0.10″…but that obviously wasn’t correct.

So how do you actually solve it?

* Ball = X

* Bat = Ball + $1

* Which means that Bat = X + $1

* Ball + Bat = $1.10

* Which means that X + X + $1 = $1.10

OK, now we can solve it:

* X + X + $1 = $1.10

* 2X = $0.10

* X = $0.05

* Which means that X + $1 = $1.05

…so the ball was $0.05, and the bat was $1.05.

The problem states two things:

1. “A bat and a ball cost $1.10 in total”

2. “The bat costs $1.00 more than the ball.”

So in other words:

1. Bat+Ball=1.10

2. Bat=Ball+1.00

So if we replaced “Bat” with “Ball+1.00” we get (Ball+1.00)+Ball=1.10, or simply Ball+Ball = 0.10, which means a ball costs 0.05 and so a bat costs 1.05.