Understanding Discounts: How to Calculate Original Prices

Have you ever stumbled upon a massive sale, and then felt like your head was spinning with all those discount percentages? You know what I mean—20% off here, 30% off there—and you just want to know... what’s the real deal? Today, let’s unravel the mystery of discounts and uncover how to calculate the original price of an item after applying that sweet discount.

Take this scenario for a spin: a television is on sale for 20% off, and the sale price is $800. What was its original price? It’s a classic question that digs into the core of how discounts work, and honestly, it’s more common than you might think. If you’re gearing up for the FSOT or just brushing up on your math skills, understanding these numeric relationships can really come in handy.

Let’s break it down—when something is marked down by 20%, that means you’re paying 80% of its original price, right? We can give that a more formal spin with a little math. Let’s call the original price ( P ). The relationship can be expressed as:

[ 0.80P = 800 ]

Now, here’s the key step: to find our elusive original price ( P ), we’ll simply divide both sides of our equation by 0.80. Easy peasy!

[ P = \frac{800}{0.80} ]

When we calculate that, we find:

[ P = 1000 ]

Voilà! The original price of the television hiked back up to $1000. And if we feel like double-checking our work, we can compute that the 20% discount amounts to $200. So when we take the original price and subtract that discount, we land right back at that sale price of $800. What a relief, right?

Now, before we move on, let’s look at the other choices we were presented with: 160, 640, and 960. Are they even close to being correct? Not at all! The calculations indicate that these numbers simply don’t align with the math behind that sale price. It’s like trying to fit a square peg in a round hole—just doesn’t work.

So, as we guide you through math problems like this, remember that the world of discounts can feel daunting at first, but with practice, it becomes second nature. Plus, mastering these skills isn’t just for the FSOT; it's a cornerstone of effective budgeting and smart shopping.

Next time you're faced with a discount tag, just remember this math. It's not only practical but kind of empowering. Instead of letting those percentages trip you up, you’ll be the one calling the shots—and putting your money to better use!