Coffee Price Calculation Based On Sugar Percentage
Hey guys! Let's break down this math problem together. It's all about figuring out the price of coffee when we know the price of sugar and what percentage of the coffee price the sugar makes up.
Understanding the Problem
So, the problem tells us that when sugar costs R$1.20 per kilogram, that price represents 40% of the price of one kilogram of coffee. Our mission is to find out how much one kilogram of coffee costs at that time. Sounds like a fun challenge, right?
Setting Up the Equation
The key here is to translate the words into a mathematical equation. We know that 40% of the coffee price is equal to the sugar price. We can write this as:
0. 40 * (Coffee Price) = R$1.20
Here, Coffee Price is what we're trying to find. The 0.40 represents 40% as a decimal (since 40% is 40 out of 100, or 40/100 = 0.40). This is super important for solving percentage problems accurately.
Solving for the Coffee Price
To find the Coffee Price, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.40:
Coffee Price = R$1.20 / 0.40
Now, let's do the math. Dividing 1.20 by 0.40 gives us:
Coffee Price = R$3.00
So, the price of one kilogram of coffee at that time was R$3.00. Pretty neat, huh?
Why This Works
The reason this works is based on the fundamental concept of percentages. A percentage is just a way of expressing a part of a whole. In this case, the price of sugar is a part (40%) of the whole (the price of coffee). By setting up the equation correctly, we can use the information we have (the sugar price and the percentage) to find the missing piece (the coffee price). Remember, this is a crucial concept in many real-life situations, from calculating discounts to understanding financial data.
Detailed Explanation
Breaking Down the Percentage
Understanding percentages is crucial for solving this problem. A percentage is a way of expressing a number as a fraction of 100. So, when we say that the sugar price represents 40% of the coffee price, we mean that if we divide the coffee price into 100 equal parts, the sugar price is equal to 40 of those parts. This can be written as a fraction (40/100) or a decimal (0.40).
Setting Up the Proportion
Another way to think about this problem is in terms of proportions. A proportion is an equation that states that two ratios are equal. In this case, we can set up the following proportion:
Sugar Price / Coffee Price = 40 / 100
We know the sugar price (R$1.20), and we want to find the coffee price. So, we can plug in the known value and solve for the unknown:
R$1.20 / Coffee Price = 40 / 100
To solve for the Coffee Price, we can cross-multiply:
R$1.20 * 100 = 40 * Coffee Price
R$120 = 40 * Coffee Price
Now, divide both sides by 40:
Coffee Price = R$120 / 40
Coffee Price = R$3.00
Again, we find that the price of one kilogram of coffee is R$3.00. Proportions can be a handy tool for solving percentage problems, especially when you're comfortable setting up the ratios correctly.
Common Mistakes to Avoid
When tackling problems like this, there are a few common mistakes that people often make. Let's go over them so you can avoid them!
- Forgetting to Convert the Percentage to a Decimal: This is a biggie! You can't directly use the percentage number (40) in the equation. You need to convert it to a decimal by dividing it by 100 (40/100 = 0.40). Failing to do so will give you a wildly incorrect answer.
- Setting Up the Equation Incorrectly: Make sure you understand what the percentage is referring to. In this case, the sugar price is 40% of the coffee price. This means the equation should be
0.40 * (Coffee Price) = Sugar Price, not the other way around. - Mixing Up the Values: Double-check that you're plugging the correct values into the equation. Make sure you know which value represents the sugar price and which value you're trying to find (the coffee price).
- Not Understanding the Problem: Before you start crunching numbers, take a moment to really understand what the problem is asking. What are you trying to find? What information are you given? A little bit of understanding can go a long way.
By avoiding these common mistakes, you'll be well on your way to solving percentage problems like a pro!
Answer
The correct answer is:
e) R$3,00
Real-World Applications
Understanding how to calculate percentages and solve problems like this isn't just about acing math tests. It has tons of real-world applications! Here are a few examples:
- Shopping: Calculating discounts, sales tax, and figuring out the actual price of an item.
- Finance: Calculating interest rates on loans or investments, understanding percentage increases or decreases in stock prices.
- Cooking: Adjusting ingredient quantities in recipes based on percentages.
- Health: Understanding nutrition labels and calculating the percentage of daily values in food.
- Data Analysis: Interpreting statistics and understanding proportions in data sets.
As you can see, percentages are everywhere! By mastering this concept, you'll be better equipped to make informed decisions in all aspects of your life.
Conclusion
So, there you have it! We've successfully calculated the price of coffee based on the price of sugar and the percentage relationship between them. Remember, the key is to understand the problem, set up the equation correctly, and avoid common mistakes. Keep practicing, and you'll become a percentage master in no time! Keep rocking, and I hope this helped you understand how to solve these types of problems better. Good luck, and happy calculating!