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## Wednesday, April 9, 2008

### Does it Come in a Box?

A certain bottle of wine costs \$10. If the wine inside the bottle is worth \$9 more than the bottle, what is the value of the bottle?

Michael said...

The value of the bottle is \$0.5 and the value of the wine is \$9.5

Ginkgo100 said...

50cent! Michael beat me to it, though.

curious said...

Tough one! 50 cents by some comments. I don't know. What is the answer?? This blog would have been excellent if the author would post the answers.

Erik said...

Curious,

I like to leave the problems without providing solutions so that readers have a chance to work on the problems without being tempted with an easy solution right away.

Fifty cents is indeed the correct answer. Using some simple algebra shows us why:

The value of the bottle = B.

The value of the wine (W) = B+9.

The total value of the bottle (B) plus the wine (W) is: B+W = 10.

W is equal to B+9 so if we substitute 'W' with 'B+9' we find that the total value is: B+B+9 = 10.

We can now subtract 9 from both sides of the equation: B+B = 1

or

2*B = 1.

Since we only have one bottle (B), not two (2*B) we divide both sides of the equation by 2 and see that the value of the bottle (B) is 0.5.

Am-Ham said...

50 cents

Anonymous said...

the value of the bottle could be any number from 1 to 99 cents. Easy

Anonymous said...

The Bottle costs \$1. Because if the bottle costs \$1 and the wine costs \$9 more than the bottle then that brings the total up to \$10 which is what it costs in the 1st place

lockiecole said...

50c