At a local department store dresses typically cost $40. however, due to a special, the dresses are reduced to $36. what percent of the original price has address been reduced to? round your answer

10% no rounding really necessary.  

Step-by-step explanation:

Percent of reduction is basically asking, what do you need to multiply the original by to get the new number.  So it's algebra.

40x = 36

x = 36/40

x = .9

So this means 36 is 90% of 40.  So how much of a percent was taken away?  10.  So that means it is 10% off.  

if it helps you can think of percent increase or decrease like this .  If you have some original value P and want to reduce/ increase by a percent x you would write it out like this.  

P + x*P = P(1+x) where of course x is negative if you are decreasing.  And you want x to be written as a decimal, so 34% would be .34  So in this case  it would look like this.

36 = 40(1-x)

.9 = 1-x

-.1 = -x

.1 = x

So that's another way to get to the answer.  

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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