Question 262679
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.