How Do You Calculate the Mass of a Single Screw from Multiple Cup Weights?

[Engage]

I have been given the masses of 5 cups, each with a different amount of screws inside.
1st cup = 13g
2nd cup = 19g
3rd cup = 8g
4th cup = 26g
5th cup = 38g

I need to find the mass of a single screw.
I was not given any equations or data besides those masses
I have no clue how to approach this, we have not done anything like it before and therefore have no skills to solve this. Please help!

 

[billiards]

first you have to make an assumption: all cups are the same weight and all screws are the same weight.

is there a common difference between these masses?

They're all integers right, so perhaps a screw weighs 1g? There's a mix of even and numbers so screw's can't weigh an even amount. Maybe they all weigh 3g, does that work? 5, 7 etc...?

Just mess around and see what you find, then in your answer explain the uncertainty and put in all the things you think it could be.

 

[DaveC426913]

What is the largest common factor of those numbers? A screw cannot weigh more than that.

 

[tim_lou]

are you given the mass of the cup? if the cups are not massless then there will be a lot of possibilities for answers. and if the mass of the screws are allowed to be non integers, the question will have an infinite numbers of answers.

 

[DaveC426913]

the question will have an infinite numbers of answers.

infinite possible answers.


Clearly the answer will have to include some assumptions and some logic to determine the most reasonable value. Given that all the data supplied are integers, I think we can manage to not overcomplicate the problem.

 

[Engage]

Thanks! I finally figured it out.

 

[Dookos]

Could you please share with us how you figured it out? I'm interested in knowing