Mastering Price Calculations: A Simple Path to Finding Original Prices

What is the first step to take when solving for the original price after a sale?

• A. Calculate the sale price
• B. Divide the sale price by the percentage off
• C. Set up the equation sale price = % x original
• D. Use the discount formula

Answer: (C)

To find the original price after a sale, setting up the equation that relates the sale price to the original price is crucial. Using the equation "sale price = percentage x original price" allows you to express the relationship between the final price after applying the discount and the original price before the discount. Typically, in such a scenario, you first determine the percentage of the original price that remains after the discount is applied. For example, if an item is sold at 20% off, then you would actually be paying 80% of the original price. By establishing this equation, it's clear how to manipulate the elements of the equation to isolate and solve for the original price. This foundational step is essential because it provides a structured approach to find the original price rather than jumping straight to calculations without context, which can lead to confusion or errors. By setting up the equation correctly, you gain clarity on how the sale price relates to the percentage of the original price, thus facilitating the correct calculation thereafter.

Finding the original price after a discount can feel like solving a puzzle, can't it? But don’t fret! We’re about to break it down step by step, making sure you’re ready for not only your everyday shopping challenges but also for that ALEKS Basic Math Placement Test looming ahead.

Let’s kick things off with the first crucial step: setting up your equation. Here’s the thing—you can’t simply plow ahead and start calculating without a clear path. The equation you’ll want to remember is "sale price = percentage x original price." This little formula is going to be your best friend when you want to unravel the mystery of how much an item cost before the markdown.

So, let’s put this into perspective. Imagine you’ve got your eye on a sleek pair of sneakers that originally costs $100 but is now sitting pretty at a 20% discount. Sounds like a deal, right? But before you grab your wallet, you want to know what you’re actually saving. By understanding the percentage you're paying after the discount—80% in this case—you set up the equation as follows:

Sale Price = 80% x Original Price

From here, it’s all about rearranging the equation to isolate the original price. That’s right! Just like a detective rearranging clues to solve a case, you’ll pull your numbers and letters around until you isolate the elusive original price.

So, to clarify further, if the sale price is $80 (what you’re actually paying), you can express this as:

$80 = 0.80 x Original Price

Now, a bit of simple algebra—just divide both sides by 0.80. And voilà! You will find that the original price was indeed $100. Pretty neat, huh?

Now, you might be wondering why this step is even necessary. Well, jumping into calculations without context is like driving with blinders on; it can lead you right into a wall of confusion or mistakes. By taking the time to establish your equation, you gain clarity—like the calm after a storm.

This approach doesn’t just work for that pair of sneakers. It applies to anything discounted! Be it a fancy gadget or textbooks for that challenging semester ahead; knowing how to find the original price gives you confidence in your spending decisions.

Let’s not forget those math tests! The Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Test likes to throw in questions about percentages and discounts. So, practicing this method of setting up equations can sharpen your skills and prepare you for success.

In summary, don’t underestimate the power of that simple equation. With practice, you’ll be flexing your math muscles, ready to tackle any question that comes your way! Remember, every calculation is a stepping stone to mastering math and feeling at ease with numbers in your everyday life.