Kerosene Tank Problem: Step-by-Step Solution

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Hey guys! Let's break down this word problem about a kerosene tank. It might seem tricky at first, but we'll solve it together step by step. This problem involves calculating how much kerosene was used from a tank over a couple of days, so stick around, and you'll ace similar problems in no time! We're going to dive deep into the problem, break it down into manageable parts, and then solve it. Ready? Let’s get started!

Understanding the Problem

First, let's make sure we fully understand the situation. The problem gives us a few key pieces of information that we need to keep in mind as we work through the solution. So, what are these pieces of information? Well, we know that initially, the cistern had 38 tons of kerosene. That's our starting point. The problem also tells us that the amount of kerosene used on the first day was 2.4 times more than the amount used on the second day. This is a crucial comparison that we'll use to set up our equations. Finally, we know that by the morning of the third day, only 9.1 tons of kerosene remained in the cistern. This tells us the total amount of kerosene used over the two days. To recap, guys, we have:

  • Initial amount of kerosene: 38 tons
  • Relationship between the first and second day's usage: First day = 2.4 * Second day
  • Remaining kerosene: 9.1 tons

Now that we've identified the key information, we can start thinking about how to use it to find our answer. The main question we need to answer is: How many tons of kerosene were used on the first day? Keep this in mind as we move forward. To solve this, we'll need to figure out how much kerosene was used in total and then use the relationship between the first and second day's usage to break down that total. Alright, let's move on to the next step: planning our approach!

Planning the Solution

Okay, guys, now that we know what we need to find, let's map out a plan to get there. Word problems can feel like a maze, but with a clear plan, we can find our way out. Here’s the strategy we'll use:

  1. Calculate the total kerosene used: We know the initial amount of kerosene and the amount remaining. The difference between these two will give us the total amount of kerosene used over the two days.
  2. Set up an equation: Let's use a variable to represent the amount of kerosene used on the second day. Since the first day's usage is 2.4 times the second day's, we can express the first day's usage in terms of the same variable. This will allow us to create an equation representing the total kerosene used.
  3. Solve the equation: Once we have our equation, we'll use algebraic techniques to solve for the variable. This will tell us the amount of kerosene used on the second day.
  4. Calculate the kerosene used on the first day: Now that we know the amount used on the second day, we can use the relationship given in the problem (first day = 2.4 * second day) to find the amount used on the first day.

This plan breaks the problem down into smaller, more manageable steps. By following this plan, we'll be able to tackle the problem systematically and avoid getting lost in the details. Remember, guys, a good plan is half the battle! Next up, we'll put our plan into action and start crunching the numbers. Let's get to it!

Step-by-Step Solution

Alright, guys, time to put our plan into action! Let's walk through each step carefully.

Step 1: Calculate the Total Kerosene Used

First, we need to find out how much kerosene was used in total over the two days. We know the cistern started with 38 tons and ended with 9.1 tons. The difference between these amounts is the total kerosene used. So, we subtract the remaining amount from the initial amount:

Total kerosene used = Initial amount - Remaining amount
Total kerosene used = 38 tons - 9.1 tons
Total kerosene used = 28.9 tons

So, a total of 28.9 tons of kerosene was used over the two days. This is a key number that we'll use in the next step. Make sure to keep track of this! Now, let’s move on to setting up our equation.

Step 2: Set Up an Equation

This is where we'll use algebra to represent the information given in the problem. Let's use a variable to represent the amount of kerosene used on the second day. A common choice is 'x', so let’s say:

x = Amount of kerosene used on the second day (in tons)

Now, we know that the amount of kerosene used on the first day was 2.4 times the amount used on the second day. So, we can express the first day's usage as:

2.  4x = Amount of kerosene used on the first day (in tons)

We also know that the total kerosene used over the two days was 28.9 tons. This means that the sum of the kerosene used on the first day and the kerosene used on the second day must equal 28.9 tons. We can write this as an equation:

x + 2.4x = 28.9

This equation represents the relationship between the kerosene used on the first and second days, and it also incorporates the total amount of kerosene used. Now that we have our equation, we can move on to solving it. Let's do it!

Step 3: Solve the Equation

Okay, guys, it's time to solve the equation we set up in the previous step. Our equation is:

x + 2.4x = 28.9

First, we need to combine like terms. On the left side of the equation, we have 'x' and '2.4x'. These are like terms because they both contain the variable 'x'. To combine them, we simply add their coefficients (the numbers in front of the 'x'):

1x + 2.4x = 3.4x

So, our equation becomes:

3.  4x = 28.9

Now, we need to isolate 'x'. To do this, we need to get 'x' by itself on one side of the equation. Since 'x' is being multiplied by 3.4, we need to do the opposite operation: divide both sides of the equation by 3.4:

4.  4x / 3.4 = 28.9 / 3.4
x = 8.5

So, we've found that x = 8.5. Remember what 'x' represents? It's the amount of kerosene used on the second day (in tons). This is a big step forward! Now, we're just one step away from finding the amount of kerosene used on the first day. Let's wrap this up in the next step.

Step 4: Calculate the Kerosene Used on the First Day

We're almost there, guys! We know that the amount of kerosene used on the second day (x) is 8.5 tons. We also know that the amount of kerosene used on the first day was 2.4 times the amount used on the second day. So, to find the amount used on the first day, we simply multiply 8.5 by 2.4:

Kerosene used on the first day = 2.4 * x
Kerosene used on the first day = 2.4 * 8.5
Kerosene used on the first day = 20.4

So, the amount of kerosene used on the first day was 20.4 tons. That's our answer! We've successfully solved the problem by breaking it down into smaller steps and using algebra to find the unknowns. Give yourselves a pat on the back!

Final Answer

Alright, guys, let's state our final answer clearly. The question asked us: How many tons of kerosene were used on the first day? We've gone through all the steps, done the calculations, and now we have our answer:

Answer: 20.4 tons of kerosene were used on the first day.

There you have it! We've solved the kerosene tank problem step by step. It might have seemed a bit daunting at first, but by breaking it down into smaller parts, we were able to tackle it effectively. Remember, the key to solving word problems is to understand the situation, plan your approach, and then carefully execute each step. You guys are now equipped to handle similar problems with confidence.

Tips for Solving Similar Problems

Now that we've nailed this problem, let's talk about some strategies you can use to tackle other word problems. These tips will help you stay organized, avoid common mistakes, and boost your problem-solving skills. So, what are these secret weapons? Let's dive in!

  1. Read the Problem Carefully: This might seem obvious, but it’s crucial. Read the problem multiple times and make sure you understand what it's asking. Identify the key information and what you need to find. Highlight important numbers and phrases.
  2. Break the Problem into Smaller Parts: Word problems often seem overwhelming because they involve a lot of information. Break the problem down into smaller, more manageable steps. This makes the problem less intimidating and easier to solve.
  3. Identify Key Information: What facts and figures are essential to solving the problem? Write them down. This helps you organize your thoughts and ensures you don't miss any crucial details. Look for keywords that indicate mathematical operations, such as “more than” (addition), “less than” (subtraction), “times” (multiplication), and “divided by” (division).
  4. Draw a Diagram or Visual Representation: Sometimes, a visual aid can make the problem clearer. Draw a diagram, chart, or graph to represent the information. This can help you see relationships and patterns that you might miss otherwise.
  5. Use Variables: If you need to find an unknown quantity, assign a variable to it. This is the foundation of algebra and helps you set up equations. Common variables include x, y, and z, but you can use any letter that makes sense in the context of the problem.
  6. Set Up an Equation: Translate the words of the problem into a mathematical equation. This is often the most challenging step, but it’s also the most important. Use the key information and variables you’ve identified to create an equation that represents the problem.
  7. Solve the Equation: Once you have an equation, use your algebraic skills to solve for the unknown variable. Follow the order of operations (PEMDAS/BODMAS) and remember to perform the same operations on both sides of the equation to maintain balance.
  8. Check Your Answer: After you’ve solved the equation, check your answer. Does it make sense in the context of the problem? Substitute your answer back into the original equation to make sure it works. If something doesn’t seem right, go back and review your steps.
  9. Practice Regularly: The more you practice solving word problems, the better you'll become. Start with simpler problems and gradually work your way up to more complex ones. Don't get discouraged if you struggle at first – everyone does. The key is to keep practicing.
  10. Learn from Mistakes: If you make a mistake, don’t just brush it off. Take the time to understand why you made the mistake and what you can do to avoid it in the future. Mistakes are valuable learning opportunities.

By following these tips, you'll be well-equipped to tackle a wide range of word problems. Remember, guys, problem-solving is a skill that improves with practice. So, keep at it, and you'll become a pro in no time!

Wrapping Up

So, there you have it, guys! We've successfully solved a word problem involving a kerosene tank, and we've also discussed some valuable tips for tackling similar problems in the future. Remember, the key to mastering word problems is to break them down into manageable steps, understand the key information, and practice, practice, practice. Don't be afraid to use diagrams, variables, and equations to help you along the way. And most importantly, don't get discouraged if you don't get it right away. Learning takes time and effort, but with persistence, you can conquer any challenge.

I hope this step-by-step guide has been helpful for you. Keep practicing, keep learning, and keep challenging yourselves. You guys have got this! If you have any questions or want to try another problem, feel free to ask. Until next time, happy problem-solving!