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JulesVerne February 13th, 2019 5:18am

In a certain country, 1/2 of 5 = 3. If the same proportion holds, what is the value of 1/3 of 10?

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ctskapski x
02/12/19 11:57 pm

Undefined
If 1/2 of 5 is 3, we can't really say 1=1, can we? So we can't know the relationship or 1/3 in relation to 1/2 from inference.

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JulesVerne Live long, and prosper
02/14/19 9:36 pm

You have to completely ignore the notion of value ordinarily placed on the numbers, and follow the algebraic rules as though they were symbols of any other kind. Just think of if 5, for example, was defined as the number obeying those properties.

ctskapski x
02/14/19 9:42 pm

Even if you take all the value and just make it letters you can't make any inferences on other aspects of it, you can really only assert one thing or another.

Taking any of the values away the question becomes

a(b/c)=d
Solve for e.

ctskapski x
02/14/19 9:43 pm

Sorry, solve for e(b/d)
Doesn't matter, though.

JulesVerne Live long, and prosper
02/18/19 8:04 am

Hm that’s a good point. I think we are supposed to assume that 10=2*5, but that isn’t made clear in the statement of the problem.

ctskapski x
02/18/19 8:39 am

(ac)(b/d)=e
a(b/c)=d
Solve for e then?

It's more math than I want to do, honestly.

ctskapski x
02/18/19 5:13 pm

Which, I guess, would come out to 1/3 of 10 being 2?

ctskapski x
02/18/19 5:16 pm

Hold on, let me check my variables

ctskapski x
02/18/19 5:17 pm

Still not sure I didn't screw up by misremembering what variables stood for what numbers, but the math is right.

ctskapski x
02/18/19 7:58 pm

Confirmed with a math teacher, it's 4.

JulesVerne Live long, and prosper
02/12/19 10:28 pm

Not a hard problem, but it’s fun to think about.