Suppose you have a large coffee can full of pennies. How can you estimate how much money the can contains without counting all the coins? (Hint: What is the relationship between the mass of pennies and the number of pennies?)

Question

kainui · Answer

Suppose you cut off one foot and weigh it. Then you cut off your other foot and put it on the scale. How much do both feet probably weigh together?

anonymous · Answer

what???

kainui · Answer

Suppose I have a keg filled with monkey brains. Now if I know 1 monkey brain is 5 pounds and I weigh the keg and it weighs 20 pounds, I know there are 4 brains in the keg because each one weight 5 pounds.

20 pounds of brains divided by 5 pounds per brain gives you 4 brains.

anonymous · Answer

what the hell man just answer my question and stop being wierd

anonymous · Answer

To answer your hint: density.

anonymous · Answer

can someone please just give me the answer -_-

radar · Answer

I would weigh the can of pennies.  I would then weigh the can.  Subtract the weight of the can from the combined weight giving you the weight of the pennies.  Then weigh one penny.  Do the appropriate math and get an answer which will be accurate if all the pennies are consistent.

anonymous · Answer

thanks

theeric · Answer

Haha, yeah.

The thing is, you have a certain number of pennies, say n (pennies).
Each one has a weight, say w (in ounces).
Then your total weight of the cup is the number of pennies times the weight of one. Say the total weight is t.

Then$$t=n*w$$
Therfore you can solve for n (number of pennies)
$$n=\frac{t}{w}$$

radar · Answer

You're welcome, and please note there may be other methods.

kainui · Answer

Methods that involve cutting off feet and weighing monkey brains?

theeric · Answer

In practice, however, you would need to know the weight of the can. It would be part of the total weight, t.

theeric · Answer

$$numberOfPennies = \frac{weight Of Pennies + weightOfCan}{weightPerPenny}$$

radar · Answer

Since the can contains a certain amount of pennies, of which some may be a rare collectors item, the amount of money they are worth is debatable.

theeric · Answer

Very true.

jagatuba · Answer

Thank you @theEric for the only truly sensible (and correct) answer in this thread. Medal to you good sir.

theeric · Answer

Thank you! :)