In this Ripley’s Believe It or Not book I have, it asks this question:
If a bottle and cork cost $1.05 and the bottle costs $1.00 more than the cork, what would be the cost of the cork?
The answer given is 2.5 cents.
Huh?
What’s to explain? Start with the cork. It costs $0.025. Then just add a dollar to get what the bottle costs. $1.05.
bottle = $1.025
cork = $0.025
Ok, hold on, see if this explains it better. Start with $1.05. You know the bottle costs $1 more than the cork so right away you subtract a $1 and are left with $0.05. Now just distribute the remaining 5 cents between the bottle and the cork (as to insure the bottle wont be less than a dollar more than the cork) and you are left with a 2.5 cent cork.
classic two equations with two unknowns
bottle + cork = 1.05
bottle = cork +1.00
substitute (cork + 1.00) into first equation
(cork +1.00) + cork = 1.05
rearrange
2cork +1.00 =1.05
cork = (1.05-1.00)/2
cork = 0.025
bottle = 0.025 +1.00 see second equation
Bottle: $1.025
Cork: $0.025
Total: $1.05
Don’t worry about it, K&K. People will forget. Eventually.
The key here is “The bottle is $1 more”
Knowing that, you can say the remainder of the bottle and the cork combined is 5 cents.
Divide that in half gives you 2.5 cents. $1 more than 2.5 cents is $1.025 giving you the price of the bottle. the remainder is the price of the cork is whats left over 2.5 cents.
It’s worded in a way to make you think you already have the price of the bottle; total price is $1.05, the bottle costs $1 more than the cork… which on the surface before thinking about it reads: “the bottle costs $1, so subtract that from $1.05 and the cork costs $0.05”. But that’s wrong of course when you try to add things back up - you aren’t given the price of either the bottle or the cork, just a comparison between the two. Work out the algebra and you come to the final answer as others have demonstrated.
The cork could be worth anything between zero cents and 5 cents.
105 cent glass, 0 cent cork
101 cent glass, 4 cent cork
102.5 cent glass, 2.5 cent cork
100 cent glass, 5 cent cork
Cecil must be choking right now. This is the SDMB?
Not to nitpick, but didn’t the original question say that the bottle costs $1 more than the cork? Your examples A, B, and D don’t fit this provision of the question.
Is it really that hard?
x = cost of cork
x + 100 (cents) = bottle
x + bottle = 105 cents
x + (x + 100) = 105
x + x + 100 = 105
2x + 100 = 105
2x = 5
x = 2.5 cents
Am I missing something that makes this difficult somehow?
I’m just glad this wasn’t the one about the three guys, the fleabag hotel, and the shifty bellboy.
I think the thing that was bothering the OP was that we don’t (at present) have a half cent coin in the US, so how would you get a 2.5 cent cork?
Of course, you could say that corks were bought in volume, say, 100 corks for $2.50. That would resolve the quandry. Either that, or the puzzle was originally written using old British money where ha’pennies were commonly used.
The cork could be worth anything between zero cents and 5 cents.
105 cent glass, 0 cent cork
101 cent glass, 4 cent cork
102.5 cent glass, 2.5 cent cork
100 cent glass, 5 cent cork
Could we use an inequality to represent this equation?
B>C<or=1.05?
These three guys walk into a hotel, and since they don’t have any money, they negotiate to pay their bill using bottles and corks … and so, what color was the bear?
woops no =
This is a brainteaser?
Maybe, but what about the two people who posted the wrong answer after the right one had been posted numerous times? How can you live that down?
Ignorance. You’re missing the ignorance.