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prealgebra intermediate

Problem

If an item is sold for dollars, there is a loss of based on the cost. If, however, the same item is sold for dollars, there is a profit of based on the cost. The ratio of is:
(A)
(B)
(C)
(D)
Solution
Let be the cost. Selling the item for dollars equates to losing of , so . Selling the item for dollars equates to profiting by of , so . Therefore . The answer is .
Final answer
A