Why is F=2, Others=3 means F is 2/3 of Others?

[happyface101]

"If F owns 2/3 of everyone else's share, how much of total share does F own?"

Solution: If F = 2, everyone else = 3, then F is 2/3 of everyone else, and thus 2/(2+3) = 2/5 of all

I'm confused by the concept in the solution - how do we know everyone is 3 and F is 2? Also even if F is 2 and everyone is 3, why is it true that F is 2/3 of everyone else? So if I have A =4, B=5, then A is 4/5 of B?? Can someone help explain the disconnect. Thank you!

[RonPurewal]

you could also use any other numbers that reduce to the fraction 2/3.
e.g.,
F = 4, everyone else = 6
F = 6, everyone else = 9
F = 212, everyone else = 318
F = 2√2, everyone else = 3√2
F = 2π, everyone else = 3π
etc.
try any of these -- you'll quickly see that you get the same reduced fraction 2/5 at the end of the day. everyone is just the same multiple of everyone else, and, once you make the fraction, those multiples will cancel each other out.

there's no compulsion to use 2 and 3 themselves; those are just the easiest values to use (and there's no reason NOT to use them, since the problem implies that the answer is a constant -- so you may as well just use the simplest values available).

[happyface101]

you could also use any other numbers that reduce to the fraction 2/3.
e.g.,
F = 4, everyone else = 6
F = 6, everyone else = 9
F = 212, everyone else = 318
F = 2√2, everyone else = 3√2
F = 2π, everyone else = 3π
etc.
try any of these -- you'll quickly see that you get the same reduced fraction 2/5 at the end of the day. everyone is just the same multiple of everyone else, and, once you make the fraction, those multiples will cancel each other out.

there's no compulsion to use 2 and 3 themselves; those are just the easiest values to use (and there's no reason NOT to use them, since the problem implies that the answer is a constant -- so you may as well just use the simplest values available).

Thank you, Ron! I'm sorry I wasn't clear in my post - I understand that 2/3 is just a ratio and thus F and Everyone Else can be anything as long as they are in the ratio of F = 2/3 Everyone Else. I was wondering if it's true that A = x, B = y, and thus A always = (x/y)*B. I should have just tested a few numbers to show that it is true and thus potentially a shortcut on the test.

For example (for the benefit of everyone else):
A = 5, B = 7 -> A = 5/7B is true because A = (5/7)*B -> 7A=5B - > 7*5 = 5*7

THUS if A=x, B=y, then A is always equal to (X/Y)*B

[RonPurewal]

ok, so it seems that you don't have any further questions here, then?

if you do, please post any further questions that you might have. thanks.