Understanding Wednesday's Merchandise Sales Expression

Which expression represents the amount of merchandise sold on Wednesday if d dollars worth of merchandise was sold on Tuesday and the amount sold on Wednesday was $150 less than twice this amount?

• A. 2d − 150
• B. 2(d − 150)
• C. 2(150 − d)
• D. 150 − 2d

Answer: (A)

To determine the correct expression for the amount of merchandise sold on Wednesday, we start with the given information. It states that d dollars worth of merchandise was sold on Tuesday. The problem specifies that the amount sold on Wednesday is $150 less than twice the amount sold on Tuesday. To express this mathematically, we first find twice the amount sold on Tuesday, which is represented as \(2d\). Then, since the amount sold on Wednesday is $150 less than this value, we subtract 150 from \(2d\). This leads us to the expression \(2d - 150\). This approach is logical because it directly follows from the relationships given—first calculating the total without the deduction, and then applying the specified reduction. In contrast, the other options misinterpret the relationships or apply operations incorrectly: - Some may involve incorrect applications of the arithmetic operations or misuses of the terms present in the question. Thus, the expression \(2d - 150\) accurately represents the situation described, providing a clear mathematical representation of the amount sold on Wednesday based on Tuesday's sales.

So, you're gearing up for that College Math Placement Test, huh? Let’s break down a question that you might see – it’s all about figuring out how much merchandise was sold on Wednesday compared to Tuesday's sales. Sounds simple, right? Well, let's dive into it!

Imagine this scenario: on Tuesday, you sold (d) dollars’ worth of merchandise. Now, here's the twist—a day later, on Wednesday, you sold $150 less than twice what you sold the day before. The challenge? To find the correct mathematical expression that represents this sales figure for Wednesday.

At first glance, it might feel a bit trial-and-error. But trust me; once you get the hang of it, this will become second nature! Let’s break it down step by step.

First off, what’s the mathematical expression for "twice the amount sold on Tuesday"? That’s easy—it's (2d). You double the amount sold on Tuesday, and voilà, you have twice Tuesday's sales in a neat package. Now, if you want to find out how much was sold on Wednesday, you need to subtract that $150 because, remember, Wednesday's sales are a tad lower.

So, we start with (2d) and take away the $150. This gives us the expression you're looking for: (2d - 150). It’s logical, straightforward, and it directly follows the information given.

But let’s think about why the other options don’t work. For instance, if you were to use (2(d - 150)), it mistakenly suggests that you first reduce Tuesday’s sales before doubling it, which isn’t what the question intended. It’s the classic case of reading comprehension – you’ve got to understand the relationships between those numbers, right?

Then there’s (2(150 - d)). Oh boy, that one misses the mark completely. It implies you’re subtracting Tuesday’s sales from $150 and then multiplying by two. Not quite what we’re after!

Let’s not forget (150 - 2d). Yikes! This one implies you’re taking twice Tuesday’s sales and subtracting all of that from $150, which doesn’t make any logical sense given our sales context.

So, why is (2d - 150) the answer we need? It's because it directly encapsulates the scenario we've talked about: starting from Tuesday's sales, doubling that figure, and making the necessary deduction for Wednesday’s sales. It keeps everything clear-cut and in alignment with how sales naturally progress through the week.

It might seem tedious at first, but take a moment to appreciate this process. It reflects real-world applications—like how businesses analyze sales trends or adjust pricing strategies based on previous sales.

Plus, understanding these types of problems prepares you for all those hidden gems in advanced topics like functions or quadratic equations! You’ll use this foundational knowledge in many ways throughout your college journey.

So next time you encounter a problem about sales or any related expressions, remember to follow the logical steps, scrutinize the wording, and you'll ace those math tests in no time. Happy calculating!