I bought a dress for 60x sold it for 500 4x at a loss of x

I bought a dress for $60x & sold it for (500 + 4x) at a loss of x%. Find the cost price

Solution

the dress is bought for $60x sold for 500 + 4x. The loss made here is x%. As an equation:

(500 + 4x - 60x)/(60x) = -x/100

=> 5000 + 40x - 600x = -6x^2

=> 6x^2 - 560x + 5000 = 0

=> 3x^2 - 280x + 2500 = 0

=> 3x^2 - 30x - 250x + 2500 = 0

=> 3x(x - 10) - 250(x - 10) = 0

=> x = 10 and x = 250/3

The price at which the dress is bought can be $600 or $5000