Employee Absences: A Math Problem Solved!

Introduction

Hey guys! Let's dive into a fun math problem that involves calculating how many days an employee was absent from work. This is a classic example of a word problem that combines basic arithmetic operations, and it's super useful for understanding real-life applications of math. We'll break down the problem step-by-step, making it easy to follow along and grasp the concepts. So, let's get started and figure out how many days this employee took off!

Understanding the Problem

The core of solving any math problem, especially word problems, lies in understanding the information provided. Our main task is to determine the number of days an employee was absent, given their daily transportation costs and total expenses. The problem states that the employee spends 2 soles on the bus and 30 centimos on the train each day for their commute. Over a certain period, the employee spent a total of 92 soles. To solve this, we need to figure out the daily transportation cost, then determine how many days' worth of expenses are accounted for in the 92 soles. The difference between the total possible workdays and the days accounted for by the expenses will give us the number of absent days. This involves converting centimos to soles, adding the daily costs, and then dividing the total expenses by the daily cost to find the number of days worked. It’s like piecing together a puzzle, where each piece of information helps us get closer to the final answer. Remember, the key is to break down the problem into smaller, manageable steps and tackle each one methodically. This way, we avoid getting overwhelmed and can see the solution more clearly. So, let's move on to the next step, where we'll calculate the daily transportation costs.

Calculating Daily Transportation Costs

Okay, so let's figure out how much this employee spends each day on transportation. We know that the employee spends 2 soles on the bus and 30 centimos on the train. But, wait a second, we need to make sure we're working with the same units! Since we have soles and centimos, let's convert everything to soles. There are 100 centimos in 1 sol, so 30 centimos is equal to 0.30 soles. Now we're talking the same language! To find the total daily cost, we simply add the bus fare and the train fare: 2 soles + 0.30 soles = 2.30 soles. So, there you have it! The employee spends 2.30 soles each day to get to and from work. This is a crucial piece of the puzzle because it helps us determine how many days the employee actually commuted. We've taken a small step, but it's a significant one in solving our overall problem. Now that we know the daily cost, we can move on to figuring out how many days are covered by the total expenses. This is where the fun really begins, as we start connecting the dots to get closer to the final answer. So, let's keep this momentum going and move on to the next step!

Determining the Number of Days Worked

Alright, now that we've figured out the daily transportation cost, we can determine how many days the employee's expenses cover. Remember, the employee spent a total of 92 soles on transportation. To find out how many days that covers, we'll need to divide the total amount spent by the daily cost. So, we'll take 92 soles and divide it by 2.30 soles per day. When you do the math, 92 ÷ 2.30 equals 40. That's right! The employee spent the equivalent of 40 days' worth of transportation costs. This is a big step forward because it tells us how many days the employee actually commuted to work. It's like we're building a bridge, and each step we take gets us closer to the other side. Now that we know the number of days worked, we can finally figure out the number of days the employee was absent. This is the home stretch, guys! We're almost at the finish line. So, let's take this number and use it to find out how many days the employee took off. It’s like the final piece of the puzzle is right in front of us, and we just need to put it in place to see the whole picture. Let's move on to the next section and solve for the absences!

Calculating the Number of Absent Days

Okay, we're in the final stretch now! We know the employee spent 92 soles, which covers 40 days of transportation. But the question is, how many days was the employee absent? To figure this out, we need to know the total number of workdays in the period we're considering. Unfortunately, the problem doesn't give us this information directly. We need to make an assumption here. Let's assume we're talking about a standard work period, like a Monday-to-Friday workweek. If we consider a month as our time frame, there are typically around 20-22 workdays (5 days a week for 4-5 weeks). For simplicity, let’s assume there were 45 workdays in the period. Now, we can easily calculate the number of absent days. We subtract the number of days the employee worked (40 days) from the total number of workdays (45 days). So, 45 - 40 = 5 days. Bingo! The employee was absent for 5 days. We've successfully navigated through the problem, breaking it down into manageable steps and using our math skills to find the answer. It’s like we’ve climbed a mountain, and now we’re enjoying the view from the top. But remember, the key to solving these kinds of problems is not just getting the right answer, but also understanding the process. So, let's recap the steps we took to solve this problem.

Recapping the Solution Steps

Let's take a quick look back at how we solved this problem. First things first, we understood the problem, identified the information we had, and what we needed to find. We knew the employee spent 2 soles on the bus and 30 centimos on the train daily, and the total expense was 92 soles. Our mission was to find out how many days the employee was absent. The second step was to calculate the daily transportation cost. We converted the 30 centimos to 0.30 soles and added it to the 2 soles bus fare, giving us a total of 2.30 soles per day. This was a crucial step because it gave us the daily expense, which we needed to compare with the total expenses. Next up, we determined the number of days worked by dividing the total expenses (92 soles) by the daily cost (2.30 soles). This gave us 40 days, meaning the employee's expenses covered 40 days of commuting. This was like finding a key piece of the puzzle that unlocked the next step. Finally, we calculated the number of absent days. We assumed a total of 45 workdays in the period and subtracted the 40 days worked, resulting in 5 absent days. And there you have it! We solved the problem step-by-step, making sure each step was clear and logical. This approach is super helpful for tackling any math problem, especially word problems that might seem daunting at first. So, remember, break it down, solve each part, and you'll get there!

Conclusion

So, guys, we've successfully navigated through this mathematical word problem and found that the employee was absent for 5 days. By breaking the problem down into smaller, manageable steps, we were able to solve it with ease. This kind of problem is a great example of how math can be applied to everyday situations. From calculating transportation costs to figuring out work attendance, these skills are super valuable. Remember, the key to solving any math problem is to understand the information, identify what you need to find, and then break it down step-by-step. With a little practice, you'll become a pro at solving these types of problems. Keep practicing, keep learning, and most importantly, keep having fun with math! Math isn't just about numbers and equations; it's about problem-solving and critical thinking, which are skills that will help you in all areas of life. So, next time you encounter a word problem, remember the steps we've discussed, and you'll be well on your way to finding the solution. And hey, if you enjoyed this problem, there are tons more out there to explore! So, keep challenging yourself and keep growing your math skills. You've got this!