Question 1062839

i think the answer will be 30% based on some other reasoning that i will detail later.


to see if this is correct, i'll use assumed numbers to see what comes out.


i'll assume the cost is 100.


if it was sold at a 16% loss, then the sale price had to be 84.


if it was sold at a 10% discount, then the retail price had to be 93 and 1/3.


this is equivalent to a retail price of 280/3.


now, if sale price is 75% of the retail price, then sale price is equal to .75 * 280/3 = 70


cost is still the same at 100.


loss is now 100 - 70 = 30


30/100 is equal to 30% of the cost.


this confirms the solution is correct.


this should be able to be done with variables instead of number.


let C = cost.
let R = retail price
let S = sale price


with a 10% discount, you get S = R - .10 * R = .9 * R.


with a 16% loss, you get S = C - .16 * C = .84 * C


we have S = .9 * R and we have S = .84 * C


this means that .9 * R = .84 * C


we can solve for C to get  C = .9 * r / .84


if we change the discount to 25%, then we get S = .75 * R


because of this change, S = .84 * C will becomes some other value times C which we don't know yet.


we'll make S = x * C


we will get:


S = .75 * R
S = x * C


since they're both equal to S, we get .75 * R = x * C


we solve for C to get C = .75 * R / x


previously we had C = .9 * R / .84


since they're both equal to C, we get .75 * R / x = .9 * R / .84


we cross multiply to get .75 * R * .84 = .9 * R * x


we solve for x to get x = (.75 * R * .84) / (.9 * R) = .7


this means that S = .7 * C


since L = (C - S) / C, we get L = (C - .7 * C) / C which gets L = .3 * C / C which gets L = .3 = 30%.


this says that you sold at a 30% loss.


30% should be your answer.