Calculating Hillary's Wage Increase A Step-by-Step Guide

Hey everyone! Today, let's dive into a practical math problem that many of us can relate to – calculating a wage increase. We're going to break down a scenario involving Hillary, who's getting a well-deserved raise, and figure out her new hourly wage. So, grab your thinking caps, and let's get started!

Understanding the Problem

The problem states that Hillary currently earns $11.25 per hour. That's her baseline, the starting point for our calculations. But here's the exciting part: Hillary is a rockstar employee! She's been exceeding her boss's expectations, which means she's in line for a 3% raise next month. Awesome for Hillary, right? Our mission is to determine exactly what her new hourly wage will be after this raise. To solve this, we'll need to understand percentages and how they apply to real-world scenarios like this one. Think of percentages as fractions out of 100. So, 3% is the same as 3 out of 100, or 0.03 in decimal form. This decimal form is what we'll use in our calculations. Many people might think, "Oh, 3% that's not much," but even small percentages can add up, especially when we're talking about something as important as our earnings. This problem isn't just about the numbers; it's about appreciating the value of hard work and how that translates into financial rewards. And for those of us looking to grow our own income, understanding these calculations is crucial for negotiating salaries and evaluating job offers. So, let's jump into the steps and see how we can help Hillary (and ourselves) figure out that new wage!

Step-by-Step Solution

Okay, let's break down how to calculate Hillary's new hourly wage, step by step. This isn't some complicated calculus; it's straightforward math that anyone can do. Trust me, you'll feel like a financial whiz after this!

1. Calculate the Raise Amount:

The first thing we need to figure out is the actual dollar amount of Hillary's raise. Remember that 3% raise? We need to apply that percentage to her current hourly wage. To do this, we'll multiply her current wage by the percentage (in decimal form). So, we take her current wage of $11.25 and multiply it by 0.03 (which is the decimal equivalent of 3%). The calculation looks like this: $11.25 * 0.03 = $0.3375. This result, $0.3375, represents the amount of the raise in dollars. It's the extra money Hillary will be earning per hour thanks to her hard work. Now, you might be thinking, "Okay, that's a small number," but it's a crucial piece of the puzzle. This step shows us exactly how much more she'll be making, and it's the foundation for finding her new total wage. We're not done yet, though! We've only figured out the raise amount; we still need to add it to her current wage.

2. Add the Raise to the Current Wage:

Now for the super satisfying part: adding the raise to Hillary's current wage to find her new hourly rate! We've already calculated the raise amount to be $0.3375. To find her new wage, we simply add this amount to her current wage of $11.25. The equation looks like this: $11.25 + $0.3375 = $11.5875. So, after adding the raise, we get $11.5875. This is very close to the final answer, but there's one little thing we need to do before we can celebrate. Remember, the problem asks us to round to the nearest cent. In the real world, wages are usually expressed in dollars and cents, so we need to make sure our answer fits that format.

3. Round to the Nearest Cent:

Okay, we're in the home stretch! We've calculated Hillary's new wage to be $11.5875, but we need to round it to the nearest cent, which means two decimal places. To do this, we look at the third decimal place (the thousandths place). In this case, it's a 7. The rule for rounding is simple: if the number in the thousandths place is 5 or greater, we round up the number in the hundredths place. If it's less than 5, we leave the number in the hundredths place as it is. Since 7 is greater than 5, we round the 8 in the hundredths place up to a 9. This gives us a final rounded answer of $11.59. And there you have it! Hillary's new hourly wage, rounded to the nearest cent, is $11.59. We've successfully navigated the math and found the solution. Feels good, right? Now, let's put it all together and see the final answer.

The Final Answer

After working through all the steps, we've arrived at the solution: Hillary's new hourly wage will be $11.59. Isn't it satisfying to solve a real-world math problem? We started with her current wage, calculated the raise amount, added it to her current wage, and then rounded to the nearest cent. Each step was crucial in getting to the correct answer. This problem demonstrates how math is used in everyday situations, from calculating paychecks to understanding discounts and sales. It's not just about abstract numbers; it's about applying those numbers to our lives. And in Hillary's case, it's about seeing the tangible result of her hard work reflected in her increased earnings. So, the next time you encounter a similar problem, whether it's figuring out a tip at a restaurant or calculating your own raise, remember these steps. You've got the skills to tackle it! Now, let's recap the key takeaways from this problem and see how we can apply these concepts to other situations.

Key Takeaways and Real-World Applications

So, what did we learn from figuring out Hillary's raise? More than just the mechanics of the calculation, we've gained some valuable insights into how math works in the real world. Let's break down the key takeaways and explore how these concepts can be applied in different scenarios. First, we reinforced the importance of understanding percentages. Percentages are everywhere – in sales, taxes, interest rates, and, as we saw, wage increases. Being comfortable with percentages allows us to make informed decisions about our finances and understand the world around us. Second, we practiced the skill of breaking down a problem into smaller, manageable steps. This is a crucial skill not just in math, but in life in general. By taking a complex problem and dividing it into smaller parts, we make it much easier to solve. Third, we saw the importance of rounding. In many real-world situations, we need to round our answers to make them practical and easy to understand. Knowing how to round correctly ensures that our calculations are accurate and meaningful. Now, let's think about some other situations where these skills can come in handy. Imagine you're shopping and there's a sale for 20% off. You can use the same principles we used for Hillary's raise to calculate the discount amount and the final price. Or, suppose you're saving for a new car and you want to figure out how much interest you'll earn on your savings account. Understanding percentages and calculations will help you project your earnings and reach your financial goals. These skills are also essential in the workplace. Whether you're negotiating your salary, budgeting for a project, or analyzing sales data, math skills are a valuable asset. So, the next time you encounter a math problem in your daily life, remember the steps we used to solve Hillary's wage increase. You've got the knowledge and the skills to tackle it with confidence!

Repair Input Keyword

What will Hillary's new hourly wage be after a 3% raise, given her current wage of $11.25 per hour? (Round to the nearest cent.)