Mastering the Border Patrol Badge Calculation

If the academy staff purchases 25 badges at $32 each with a 20% discount, what is the total amount spent on badges?

• A. $800
• B. $790
• C. $640
• D. $16

Answer: (C)

To find the total amount spent on badges, it's important to first determine the total cost without the discount. The price of each badge is $32, and with 25 badges being purchased, the initial calculation would be: Total Cost = Number of Badges × Price Per Badge Total Cost = 25 × 32 = $800 Next, we need to apply the 20% discount to the total cost. A 20% discount means you retain 80% of the total cost. To calculate this: Amount after discount = Total Cost × (1 - Discount Rate) Amount after discount = $800 × (1 - 0.20) Amount after discount = $800 × 0.80 Amount after discount = $640 Thus, the total amount spent after applying the discount for the badges is $640. This calculation reflects the correct understanding of how discounts work, confirming that the total expenditure on the badges, considering the provided discount, is correct.

When preparing for the Border Patrol exam, it’s crucial to grasp fundamental math skills, particularly those involving costs and discounts. Take, for instance, a real-world scenario involving badge purchases—it's not just about numbers; it’s about making smart financial decisions. Let’s walk through a problem that could easily pop up in your studies or even your daily life.

Okay, picture this: the academy staff wants to order 25 badges priced at $32 each. Sounds straightforward, right? But wait! There’s a 20% discount on the total purchase. So, how do you calculate how much is actually spent? Let me explain.

First off, we need to figure out the total cost before applying any sort of discount. The initial equation is as simple as it gets:

Total Cost = Number of Badges × Price Per Badge

So, plugging in our numbers:

Total Cost = 25 × $32 = $800.

Bam! That’s $800 staring us in the face. But, alas, discounts are like that friend who shows up at the party uninvited but ends up being the life of the event. You have to consider it.

Now, here's how to calculate the total amount after the discount. Remember, a 20% discount means you’re going to pay 80% of the total cost. Let’s calculate it together:

**Amount after discount = Total Cost × (1 - Discount Rate)

Amount after discount = $800 × (1 - 0.20)**

Amount after discount = $800 × 0.80 = $640.

And there you have it! The final cost for those 25 badges comes to $640.

This calculation isn't just a number—it reflects the understanding that discounts can significantly impact budgeting. But don’t you just feel a twinge of excitement knowing that you've wrapped your head around this math? Every one of these problems prepares you for real-life financial decisions.

But what does this really teach us? It’s all about making informed choices, whether in a professional atmosphere or simply when shopping. Understanding how to apply percentages, dissect costs, and manage budgets serves as foundational skills, not just for the Border Patrol exam but for life in general. Who knew that learning about badges could have such far-reaching impacts?

Next time you're faced with a math problem, be it on the exam or out in the world, remember this badge scenario. Approach it with confidence, breaking down the problem as we have, and you’ll find answers more accessible.

In conclusion, whether you're prepping for the Border Patrol exam or just sharpening your math prowess, remember to keep your calculations clean, and don't forget to take those all-important discounts into account. You’re not just studying math; you’re developing a practical skill set for your future career. Now that's something to badge about!