Author Topic: Riddle - A man goes into a N.H. sporting goods store... (Read 1789 times)

TKGS · « **Reply #5 on:** June 23, 2016, 07:16:00 PM »

Quote from: Matthew

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

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

Given the youtube interviews of college students of late, I can believe a lot of them get this one wrong.

Neil Obstat · « **Reply #6 on:** June 24, 2016, 08:13:59 PM »

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!

TKGS · « **Reply #7 on:** June 24, 2016, 09:23:27 PM »

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.

Neil Obstat · « **Reply #8 on:** June 24, 2016, 09:56:18 PM »

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.

qeddeq · « **Reply #9 on:** June 25, 2016, 12:04:38 AM »

or let X= the price of the ball in pennies, then 110= (x+100) +x, so 2x+100=110, so x=5, or 5 pennies, the bat is 5 pennies plus 100 pennies(one dollar), =105 pennies 1.05 dollars. Now add in inflation at 2000% ...