SOLUTION: Sassy Fashions buys dresses at wholesale and then marks them up for retail sale. They recently sold a dress at a 40% discount off of their marked-up price. What percent mark-up did

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Sassy Fashions buys dresses at wholesale and then marks them up for retail sale. They recently sold a dress at a 40% discount off of their marked-up price. What percent mark-up did      Log On


   

Question 262679: Sassy Fashions buys dresses at wholesale and then marks them up for retail sale. They recently sold a dress at a 40% discount off of their marked-up price. What percent mark-up did they originally apply to the dress if they broke even on the sale? Express your answer to the nearest whole percent
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
markup price = x

dress sold at x - .4*x = .6*x

cost of the dress = c

they broke even after selling the dress.

this means that:

c = .6*x

solve for x to get:

x = c/.6

this is the same as x = 1/.6 * c which is the same as 1.66666666 * c.

.66666666... is the same as 2/3.

they originally marked the dress up by 2/3 of the cost of the dress.

here's how it works:

assume the original cost of the dress was 12 dollars.

they marked it up by 2/3 of the cost = 2/3 * 12 = 24/3 = 8.

the marked up price of the dress is 12 + 8 = 20 dollars.

they discounted 40% off the marked up price.

the dress is now 20 dollars minus .4 * 20 dollars.

since .4 * 20 = 8, this becomes:

20 dollars minus 8 dollars = 12 dollars.

the dress is sold at cost.

your answer is:

they marked the dress up by 67%

2/3 = .66666666... * 100% = 66.666666...% = 67% rounded to the nearest integer.