Is There More Salt in the Pepper Shaker Or Pepper in the Salt Shaker?

Sample Tutorial Question

You have a salt shaker and a pepper shaker. You take a spoonful of salt and put it in the pepper shaker. You then take a spoonful from the pepper shaker and put it in the salt shaker.

Is there more salt in the pepper shaker or pepper in the salt shaker?

Explain

Does it matter how big the shakers are?

Does it matter how big the spoon is?

Does it matter if you shake up the pepper shaker before scooping?

Presenter, read the following:

The original question asked, “Is there more salt in the pepper or more pepper in the salt?” I figured that since I put pure salt in the pepper and a mixture of salt and pepper in the salt, that there would be more salt in the pepper shaker.

I got marked wrong on the assignment. My point of confusion is, there isn’t any information given. How do I calculate this without any numbers?

What questions do you have to help me through this?

Tutorial Answer

There is exactly the same amount of salt in the pepper shaker as there is pepper in the salt shaker no matter the size of the shakers, the scoop, or whether the second shaker was mixed or not.

Here’s why. . .

1)  Let’s say that the spoon holds 10 mL. If you transfer 10mL of salt to the pepper shaker, there will temporarily be 10 mL of salt in the pepper shaker.

2)  If your spoon now picks up 8mL of pepper and 2mL of salt, there will be 8mL of salt left in the pepper.

3)  When the scoop is dumped into the salt shaker, there will be 8mL of pepper in the salt shaker.

4)  No matter what, there will always be equal amounts in each because the amount of salt in the pepper is S-x and the amount of pepper in the salt is S-x where S is the size of the spoon and x is the amount of salt included in the second scoop.

Example:

Original shakers Spoonful of 4 salt transferred 4 particles moved back 3:1

Original shakers Spoonful of 4 salt transferred 4 particles moved back 2:2

Original shakers Spoonful of 4 salt transferred 4 particles moved back 1:3

No matter what, the amounts are equal. The size of the spoon would change the number of particles moved, but not the ratio. Mixing wouldn’t matter. Size of the shaker doesn’t matter either.

Remember during the tutorial to “ask don’t tell” at all times. At the end, check to make sure that the presenter truly understands and that they can list the steps in the process of solving the problem.