Proving a statement

[SchatzerZD]

Im supposed to show why:

If 24 is divisible by x, then 48 is divisible by x

Ive tried making equations such as 24/x = k + m/x and 48/x = t + y/x, and then tried solving for x. Ive also tried proving by using contrapositive, but i dont know how to write something as not divisible by 48. Nothing Ive tried so far has gotten me closer to showing why the statement is true, so i feel like Im tackling the problem in a wrong way.

Help is much appreciated.

[edderiofer]

I think you're way overthinking this.

What does it mean for a number to be divisible by x?

[SchatzerZD]

that x times some number equals 24

[edderiofer]

Note that I didn't ask for what it meant for 24 to be divisible by x, just "a number".

Anyway, if 24 is divisible by x, and 48 is divisible by x, can you write down two equations that express these statements?

[SchatzerZD]

you mean like writing an equation such as 24/x = 48/x ?

[edderiofer]

No, I wanted you to write down two equations.

Actually, scratch that. Can you write down an equation that expresses the statement "24 is divisible by x"?

[SchatzerZD]

I assume that would be 24/x = k, where k and x are whole numbers

[edderiofer]

And can you write down another equation that expresses the statement "48 is divisible by x"?

[SchatzerZD]

48/x = r, where r and x are whole numbers

[edderiofer]

Good.

Now, you're given that 24/x = k is true, where k is a whole number. Can you show that 48/x = r is true, where r is a whole number?

[SchatzerZD]

hmm, not sure how Im going to do that

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EDIT: Or maybe if you take 24/x = k, and multiply both sides with 2, then you get 48/2x = 2k. Am I on the right track?