...and he picks up a baseball and a baseball bat, and buys them at the register.  The total price of the two items was $1.10, but the bat cost $1 more than the ball.  

Since this store was in New Hampshire, there was no sales tax.  Live Free or Die.  :reporter:

How much did the ball cost?

This one is too easy.  It's simply algebra.  Shall I produce the equation?

That's the way I did it too:

T = A + B;  where A = B + $1;  Total = $1.10, bAt, Ball.

Sum of equations.

Solve for B.

But simpler still, you don't even need algebra.

It's $1.05 for the bat and 0.05 for the ball.

This is the trick question that many college students get wrong.

It has to do with human psychology and shortcuts our minds take.

I thought $1.00 & 0.10 at first, too. But those aren't $1 apart :)

Excellent!  

The man who told me this says that at least 9 out of 10 people at large go for the  $1.00 and $0.10, without checking their answer for the requirement of $1 difference.  They confuse "Bat and Ball" with "Total less the Ball."  Like you say, in an effort to be clever, the mind makes a shortcut into a logical error, and "drops the ball" by forgetting that the Bat costs a dollar MORE than the Ball.  It seems easier to separate a dollar from ten cents in $1.10, than to separate a dollar-five-cents from 5 cents in $1.10.

It's not really a trick question, because everything is right there in front of you.  Like a chess game:  it's all in the open!  Nothing to hide.

I would never post a trick question!!  HAHAHAHA

I heard this from a friend, and about a year later when I reminded him about it, he insisted that the total price had been $1.05 all along.  I suspect he got mixed up over the past year, because he has been known to forget details like this, in other things.  But he can readily take any new riddle and solve it very fast, so long as it's not deceptively tricky (such as the bicycles in the alley one, for instance).

When I told him that $1.05 effectively makes for a new problem, he denied it.  I then gave him the correct answer for the new problem and challenged him to show me any such pricing on any item in any store in town, and he changed the subject (I guess he is unwilling or else unable to do that).

Can anyone say what the new prices would be for a total price of $1.05, and the Bat is still $1 more than the ball?


TKGS:  This would be an opportunity for you to show how your formula works!

Let X=the price of the ball.  Therefore, the price of the bat=X+1.

The algebraic formula is:  X + (X + 1) = $1.05 (or, whatever the total price is).

Solve for X.  Since addition is commutative, the parentheses can be eliminated.

X + X + 1 = $1.05.  Group the variables:  2X + 1 = $1.05.

Subtract 1 from each side of the equation:  2X = $0.05.

Divide both sides of the equation by 2:  X = $0.025, or 2-1/2 cents.

The bat must therefore equal $1.025.  

The total cost is $0.025 + $1.025, or $1.05.

Very good.  That's simpler than my method.  

Without algebra, however, the idea of dividing in half the difference between the total price and the $1 does the same thing. For a total price of $1.10, the difference is 10 cents, which when divided in half you get 5 cents for the ball.  For a total price of $1.05, the difference is 5 cents, and dividing that in half gives 2-1/2 cents for the ball.  

I've never seen a price tag like that. And for the riddle to make sense, the bat must have a price, and the ball would need its own price. If you wanted to buy just one ball, how would they charge you 2-1/2 cents for it? You would have to pay 3 cents, so the ball no longer costs 2-1/2 cents.

The principle of dividing an amount in half to distribute evenly works in other problems, as well.

Quote from: TKGS

Let X=the price of the ball.  Therefore, the price of the bat=X+1.

The algebraic formula is:  X + (X + 1) = $1.05 (or, whatever the total price is).

Solve for X.  Since addition is commutative, the parentheses can be eliminated.

X + X + 1 = $1.05.  Group the variables:  2X + 1 = $1.05.

Subtract 1 from each side of the equation:  2X = $0.05.

Divide both sides of the equation by 2:  X = $0.025, or 2-1/2 cents.

The bat must therefore equal $1.025.  

The total cost is $0.025 + $1.025, or $1.05.

Very good.  That's simpler than my method.  

Without algebra, however, the idea of dividing in half the difference between the total price and the $1 does the same thing. For a total price of $1.10, the difference is 10 cents, which when divided in half you get 5 cents for the ball.  For a total price of $1.05, the difference is 5 cents, and dividing that in half gives 2-1/2 cents for the ball.  

I've never seen a price tag like that. And for the riddle to make sense, the bat must have a price, and the ball would need its own price. If you wanted to buy just one ball, how would they charge you 2-1/2 cents for it? You would have to pay 3 cents, so the ball no longer costs 2-1/2 cents.

The principle of dividing an amount in half to distribute evenly works in other problems, as well.

Gasoline is sold like that all of the time ($2.299/gal). As long as you buy both the bat and ball, your total would be $1.05. You'd only have to round if you only bought one item.