Originally posted by mouse
how are these possible:
(.4 + .1) / (.4 + .2) = 2 1/3
and
140/1 = .5Y - 10(.1) = 282
OMG... this is starting to get a bit ridiculous in a way... or weird at least... (and since you put this in a maths extension forum).
The first equation is absolutely impossible UNLESS you either:
1. make a new set of rules governing the operations of addition and division
2. make a new definition on the meaning of symbols, for example, "/" doesn't mean "divided by"
3. do both point 1 and point 2
Anyway, let's make it clear of why it's not possible:
(.4 + .1) / (.4 + .2) = 2 1/3
0.5 / 0.6 = 2 1/3
0.5 / 0.6 = 7 / 3
5 / 6 = 7 / 3
BUT, assuming you don't do any of points 1-3 above, 5 / 6 is not equal to 7 / 3. Quite easily, 5 / 6 is less than 1 while 7 / 3 is more than 1.
Now, the second equation:
140/1 = .5Y - 10(.1) = 282
I prefer to break this down to three sub-equations:
140/1 = .5Y - 10(.1)
140/1 = 282
.5Y - 10(.1) = 282
The first sub-equation is possible for certain value of Y. So is the third sub-equation. However, we can deduce that the second sub-equation is not true, therefore the overall equation, 140/1 = .5Y - 10(.1) = 282, is not true and there is no solutions to it.
Do I make sense? Well, I'm just a bit bored at the moment so sorry if I seem too wordy...