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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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.