Suits at a local clothing store are discounted 20%. Despite the discount, the store owner enjoys a net profit (discount price minus cost) equal to 60% of the cost of the suits. If the suits cost the clothing store owner $200 each, what was the prediscount price of each suit?

The answer key says..
x=the prediscount price of a suit
0.8x= discount price

0.8x-200=0.6•200
x=$400

I don't get where the 0.8 in 0.8x came from..how come the discount price =0.8??

WAIT,I think I got it!
But please check my reasoning..

x-0.2x=discount price
1-0.2=0.8!!!!! Correct????

correct

Yes, you got it! Your reasoning is correct.

The 0.8 in 0.8x represents a 20% discount, which can also be expressed as 1 - 0.2. So when you subtract 0.2x from x, you are essentially calculating the discount price. Subtracting 0.2x from x gives you 0.8x, which is the discounted price (80% of the original price).

In this case, the equation x - 0.2x = discount price simplifies to 0.8x = discount price.