How do you figure out the original price of something that you only know the ending total and the percentage off?

Answer 1

We're gonna tear this up. It's simple, but it will take a bit of patience, so buckle up. Ready? Let's go. You don't know the original price. You know the percent off. You know the sale price. We're in business. Let's hammer this thing. Here's how to work the problem....

We don't know the original price, but we know that a percentage of it has been deducted from it (that original price) to give us a sale price, okay? Some percent off the original price is the sale price. Here's the trick. Look at the percent off. Now look at 100% minus the percent off. This new percentage represents how much of the original cost the final cost is. Got it? Another way to say that is that our new (calculated) percentage times the original price equals the sale price. Make sense? Let's pick something easy and give it a test drive.

Say something costs $9 (that's the sale price), and it was marked down 10%. That means that the original cost minus 10% of the original cost is the final (the sale) price, or the $9. Now check this out. Focus. The discount was 10%, and another way to look at the problem is that the sale price is 100% -10% of the original price, which says that the sale price is 90% of that original price. Again, the sale price is 90% of the original price. See how that works? We use the discount (percentage) and make a calculation to find out how much of the original price the sale price is. We good? Super.

As we now have a "new" set of facts to work with, that is, we have the sale price and the percentage of the original price that the sale price represents, we can go for it. The original price (the unknown) times the percentage of that original price that the sale price represents equals the sale price. Let's look at our example.

The original price times the percentage of that price the sale price represents equals the sale price. Again, original price times that percentage we calculated equals the sale price. Now to do some math. If the original price times that new percentage equals the sale price, then the original price equals the sale price divided by the percentage. See what we did? We moved the percentage over to the other side of the equation. We divided both sides by the percentage, and it "dropped out" on the one side and appeared on the other. That's because we needed to isolate the original price (so we could solve for it using the other variables). In our example, the original price equals $9 (the sale price) divided by 90% (the percentage of the original price the sale price represents. $9 divided by 90% equals $9 divided by 0.9 which equals $10. The original price of the item was $10, and it was 10% off. The 10% of $10 equals $1, and the sale price is $10 minus $1 which equals $9. Our work checks.

One more problem for fun to lock things in. At a 20% off sale, an item sells for $40 (its sale cost). What was its original cost? We know that the $40 represents 80% of the original price (100% -20%). The original price times the 80% equals $40. The original price equals $40 (the sale price) divided by the 80% (the percentage of the original price that the sale price represents). $40 divided by 80% equals $40 divided by 0.8 which equals $50. Our item's original price was $50. Last thing. $50 times 20% equals $10, and $50 minus $10 equals $40. Our work checks.

We good? Excellent!

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