SOLUTION: A dress goes on sale at 25% off the original price. The next day it drops 20% from the current price, the following day the price drops another 25% from the current price. The fin

Question 936262: A dress goes on sale at 25% off the original price. The next day it drops 20% from the current price, the following day the price drops another 25% from the current price. The final price is 27 dollars. What was the starting price of the dress?
Please show work.
Thank You.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x represent the original price of the dress.

it goes on sale for 25% off the original price.

if you're taking off 25%, then what you are left with is 75%.

the sale price is therefore 75% of x which is equal to .75 * x

the next day it drops 20% from 75% of x.

if you're taking off 20%, then what you are left with is 80%.

the sale price is therefore 80% of 75% of x which is equal to .8 * .75 * x.

simplify .8 * .75 * x to get .6 * x which is equal to 60% of x.

the next day it drops another 25%.

if you take off 25%, then you are left with 75%.

the sale price is therefore 75% of 60% of x which is equal to .75 * .6 * x.

simplify .75 * .6 * x to get .45 * x which is equal to 45% of x.

the final price is equal to 27 dollars, so you get:

45% of x is equal to 27 dollars which becomes:

.45 * x = 27

divide both sides of this equation by .45 to get:

x = 27/.45 which becomes:

x = 60 dollars.

the original price of the dress was 60 dollars.

25% of 60 = 15 dollars.
take 15 dollars off of 60 and you get the new sale price of 45 dollars.

20% of 45 = 9 dollars
take 9 dollars off of 45 dollars and you get the new sale price of 36 dollars.

25% of 36 dollars = 9 dollars.
take 9 dollars off of 36 dollars and you get the final sale price of 27 dollars.

numbers check out so you're good.

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