If A is 15 percent more than B....

[ghong14]

If A is 15 percent more than B and A is 115. What is B?

This is a simple question but more of a conceptual issue for me.

To set this problem up you would write A = 1.15 B; A is 115; 115=1.15 B Therefore B is equal to 100. Why can't we just say that B = .85A. I know that mathematically this does not work out but I wanted to see what the conceptual explanation is considering that we can say that X's decreased by 20% therefore Xfinal is .8x?

Thanks.

[RonPurewal]

If a is 15% more than b, then the difference is 15% of b.

If b is 15% less than a, then the difference is 15% of a.

Not the same. The second difference is bigger.

[RonPurewal]

By the way, this is totally the kind of thing you can figure out by yourself. Just get a little dirty -- i.e., play around with some numbers and watch what they do.

Like, say I start with 100.
If I increase that by 20%, I gain 20, for a total of 120.
If I decrease that by 20%, whoa! I lose 24, for a total of 96.

Just look at a couple of examples like that ^^ and it will be pretty easy to see what is going on.
(Then reverse the order of the increase and the decrease, and you'll notice pretty much the same thing.)