ms.gonzalez wanted to buy a book that was on sale 25% off the original price. the bookstore was offering an additional 20% off to customers who used store credit cards. after all the discounts, ms. gonzalez paid $24.00 for the book. what was the original price in dollars?

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ms.gonzalez wanted to buy a book that was on sale 25% off the original price. the bookstore was offering an additional 20% off to customers who used store credit cards. after all the discounts, ms. gonzalez paid $24.00 for the book. what was the original price in dollars?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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let the original price be x, then 24=x-0.25x-0.20x --> 24=0.55x ---> x=$43.6
i dont understand
x × (1-0.25) × (1-0.20) = 24 24 ÷ 0.80 ÷ 0.75 = 40 AnwarA's error is that the -0.020x term should be -(0.022×0.020)x, because the second discount is cumulative with the first. The total discount is 1-(1-0.25)×(1-0.20) = 1-0.75×0.80 = 1-0.60 = 0.40; the original price is 24 ÷ 0.60 = 40; the discounted price is 40 × 0.60 = 24 and the discount amount is 40 × 0.40 = 16.

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err... typos; that should say "the -0.20x term should be -(0.25×0.20)x"
i am still confused is their an easier way to explain it
A percentage discount reduces the price by some factor less than one; e.g. 20% of x is x⋅0.20, so 20% off x means the price goes down from x to x-x⋅0.20, or, by the distributive property, the price goes down to x⋅(1-0.20). This can be repeated to apply multiple discounts. This question asks you to reverse the process - to take the discounted price and find the original price, like solving 24=x⋅(1-0.20) for x. Naturally, x = 24÷(1-0.20), and again you can repeat this for multiple discounts.

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