SOLUTION: If the cost of a cell phone has decreased 400% during the past 10 years, does that correspond to a cost decrease of four times?

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Question 496708: If the cost of a cell phone has decreased 400% during the past 10 years, does that correspond to a cost decrease of four times?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i'm not sure you can say that.
here's why:

suppose the cost was $500 per month 10 years ago.
suppose the cost is now $100 per month.
the cost has decreased by the following formula:
$500 - x*$500 = $100
add x*$500 to both sides of this equation and subtract $100 from both sides of this equation and you get:
$500 - $100 = x*$500
combine like terms to get:
$400 = x*$500
divide both sides of this equation by $500 to get:
$400 / $500 = x which results in:
x = 4/5 which is equal to 80%.

the original formula of:
$500 - x*$500 = $100 becomes:
$500 - .8*$500 = $100 which becomes:
$500 - $400 = $100 which becomes:
$100 = $100 which is true, confirming the value of x = .8 as good.

if you are looking at an increase in price, then the percentage figure can go higher than 100%.

]if you are looking at a decrease in price, then the percentage figure has to be less than 100%, otherwise the cost goes to 0 or below which is not good for business.

if you say that the previous price was 400% more than the current price, then you are talking about something entirely different.

now the formula becomes:

p = c + 4c which results:
p = 5c

this says that the previous price was 5 times the current price.
let's see if this works.

assume the current price is $100.
if you say the previous price was $400 more than that, then the previous price was equal to $500.
that equates to a price that is 5 times the current price.

the numbers are very tricky to work with, so you have to be careful how you express what you are trying to say.

you can say that the previous price is 400% higher than the current price, but you can't say that the current price is 400% lower than the previous price.

that's my thinking.
i think i know what you meant, but it is technically wrong to express it the way that you did.

you can add more than 100% of the previous price and get a valid answer.
you can't subtract more than 100% of the previous price and get a valid answer.
the answer will be negative which you do not want to do unless you are paying people to take the product off your hands.