Question 902568
rate = percent / 100%.


50/3 percent means a rate of 50/300 which is a rate of 1/6 after you simplify it.


loss = 50/3 percent of cost translates to:


loss = 1/6 * cost


this means that loss / cost = 1/6.


we want to find loss / sales


we know that sales = cost - loss


so loss / sales is equivalent to loss / (cost - loss)


we know that loss is equal to 1/6 * cost, so the equation becomes:


loss / sales = loss / (cost - loss) = loss / (cost - 1/6 * cost) which becomes:


loss / sales = loss / (5/6 * cost)


since loss is equal to 1/6 * cost, we get:


loss / sales = (1/6 * cost) / (5/6 * cost) which becomes:


loss / sales = 1/5 which is equal to 20%.


let's see if this works.


you take a loss of 50/3 percent of cost.


let's assume your cost is 1200 dollars.


you take a loss of 50/3 percent of the cost which is a loss of 200 dollars.


200 / 1200 = 1/6 which is equal to 100/6  percent which is equal to 50/3 percent so the numbers check out.


so you took a loss of 200 dollars and your cost was 1200 dollars which means you sold for 1000 dollars.


the percent loss on sales is therefore 200 / 1000 = .2 which is equal to 20%.


i believe that's the figure we calculated above so the formula is good.


your solution is:


a loss of 50/3 percent on cost is equivalent to a loss of 20% on sales.