Question 1072148
two ways to look at this because i'm not understanding exactly what you're looking for.


does he want to make 10% gain on the remaining 2/3, or does he want to make 10% gain on the whole thing?


i'm assume he wants to make 10% gain on the whole thing, including the part where he took a 10% loss.


if that's not what you want, then let me know and i'll re-work the solution accordingly.


he has merchandise that cost him 3000.


he sells 1/3 of this at a loss of 10%.


1/3 * 3000 = 1000 from which he received revenue of 900 which gave him the 10% loss of 100.


he has 2/3 of the 3000 left which means he has 2000 worth of merchandise left to sell.


he wants to make an overall gain of 10% on the 3000 worth of merchandise.


10% of 3000 is equal to 300.


the total gain he wants to make is 300 from the remaining 2000.


he wants to sell the remaining 2000 at a 20% discount from the retail price.


what he is saying is that the selling price has to be 80% of the retail price.


to make a profit of 300, then the selling price minus the cost of 2000 must be equal to 300.


let R equal the retail price and let S = the selling price and let C = the cost and let P equal the profit.


the equation would start out as S - C = P


this means selling price minus cost = profit.


since S = .80 * R, the equation becomes .80 * R - C = P


this means 80% of the retail price minus the cost is equal to profit.


since P = 300 and C = 2000, the equation becomes .80 * R - 2000 = 300


add 300 to both sides of this equation to get .80 * R = 2300.


divide both sides of this equation by .80 to get R = 2300 /.8 = 2875.


the retail price has to be 2875.


discount is 20% of 2875 = 575.
2875 - 575 = 2300.


selling price is equal to 2300.


cost of the remaining merchandise is 2000 which makes the profit = 300.


original cost is 3000.


profit is 300.


percent profit is 300 / 3000 * 100 = 10%.


by charging a retail price of 2875 for the remaining 2000 worth of merchandise, he can give a 20% discount to make the selling price 2300 which gives him 300 profit which is 10% of the overall cost of 3000 worth of merchandise.


at least, i think this is what you're asking.


if different, let me know what's different and i'll rework it for you based on that new understanding.