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.
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
The value of the bottle is $0.5 and the value of the wine is $9.5
ReplyDeleteAny other possible answer?
50cent! Michael beat me to it, though.
ReplyDeleteTough 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.
ReplyDeleteCurious,
ReplyDeleteI 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.
50 cents
ReplyDeletethe value of the bottle could be any number from 1 to 99 cents. Easy
ReplyDeleteThe 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
ReplyDelete50c
ReplyDelete