# If x is to be increased by 400%, is that expressed as 4x or 5x?

If "x" is to be increased by 400%, is that expressed as 4x or 5x?

If "x" is to be increased by 400%, is that expressed as 4x or 5x???

Thanks.

berkeman
Mentor
It can be open to interpretation, but I believe that the mathematical convention (as opposed to the clothing store convention) would be:

An increase in x by 400% means that you now have 100% of x plus 400% of x (the increase is the 400% on top of the initial 100%). So you have 5x after that increase.

The basic fact is that if X is increased by 100%, that can not be X, it must be 2X. This leads to a 400% increase results in 5X.

However, as berkeman points out, not everybody sees it that way. If someone offers you 500% on your investment, you'd might have to ask if that means to return 5X or 6X, since these kind of figures are put out without much thinking going on.

A reason for this confusion is, for example, in dice of being paid odds of 1-1, which obviously mean returning 2X. So that if odds in dice are 5 TO one, the return is 6X. But if the matter is expressed as 5 FOR 1, then the return is 5X.

There is some logic in this because if in dice the payoff is 3 to 1, then the dealer places three stacks of chips next to your stack on the table when you win, and you take all.

But take the matter of a video poker machine. If the payoff is 9 for a Full House, this means you get nine coins back on playing one coin. The original investment is expended at once and is thought of as the property of house. This situation leads to the amazing fact as one writer saw it, that if you win 1, then lucky you! investing one coin, you are now a "winner;" you got your own coin back! )

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