Solving A Money Puzzle How Much Do Sutopa Maneet And Kim Have

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Hey guys! Let's dive into a fun math problem where we need to figure out how much money Sutopa, Maneet, and Kim each have. It's like being a detective, but with numbers! We will break down the problem step by step, making it super easy to understand. Let's get started!

Breaking Down the Problem

So, the main question we are trying to answer is: How much money does each of them have? To solve this, we have a few clues. First, we know that Sutopa has 34\frac{3}{4} of the money Maneet has. Second, Maneet has $18 less than Kim. Third, together, they have $286.40. These clues are like pieces of a puzzle, and we need to put them together to find the solution. Let's take a closer look at each clue to understand what it means and how it helps us.

Sutopa's Money

In this section we are going to focus on the first clue, which is about Sutopa’s money. We know that Sutopa has 34\frac{3}{4} of the money Maneet has. What does this mean? It means if we divide Maneet's money into four equal parts, Sutopa has three of those parts. This is a fractional relationship, which might sound complicated, but it's just a way of comparing how much money each person has in relation to each other. Let's say Maneet has a certain amount of money, we can represent this as a whole, or 1. Sutopa has 34\frac{3}{4} of that whole, which is less than what Maneet has. This piece of information is crucial because it helps us relate Sutopa's money to Maneet's money. We can use this relationship to write an equation later on, which will help us solve the problem. Remember, the key here is that Sutopa's amount is directly tied to Maneet's amount, so if we can figure out how much Maneet has, we're one step closer to finding out how much Sutopa has. This is like finding one piece of the puzzle that connects to another piece. Understanding this relationship is essential for solving the problem.

Maneet's Money

Now, let's look at the second clue, which is about Maneet's money. We know that Maneet has $18 less than Kim. This clue gives us another relationship, but this time it's between Maneet and Kim. It tells us that if we know how much money Kim has, we can easily find out how much Maneet has by subtracting $18. This is a direct comparison in terms of a dollar amount, making it a bit more straightforward than the fractional relationship between Sutopa and Maneet. For example, if Kim has $50, Maneet would have $50 - $18 = $32. This relationship is super important because it allows us to express Maneet's money in terms of Kim's money. Just like the previous clue, this will be helpful when we start writing equations to solve the problem. It's like finding another connecting piece for our puzzle. The difference of $18 is the key here, and it helps us link Maneet's money to Kim's money. So, keep this relationship in mind as we move forward.

The Total Amount

Let's focus on the third clue in this section. The third clue is a big one: Together, they have $286.40. This clue tells us the total amount of money that Sutopa, Maneet, and Kim have combined. This is a total value that we can use to create an equation involving all three people. It's like having the final border of our puzzle, which helps us fit all the pieces inside. This total amount is crucial because it gives us a concrete number to work with. We know that the sum of Sutopa's money, Maneet's money, and Kim's money must equal $286.40. This allows us to bring all the individual relationships we've discussed together into one equation. This equation will be the key to unlocking the solution because it ties everything together. Remember, this total amount is the glue that holds all the pieces of the puzzle together. It's a fixed number that we can use to check our answers later on, making sure our solution makes sense.

Setting Up the Equations

Okay, now we're going to turn these clues into math equations. This is where the fun really begins! We'll use letters to represent the unknown amounts of money each person has. Let's use S for Sutopa's money, M for Maneet's money, and K for Kim's money. By using these variables, we can write equations that represent the relationships we discussed earlier. This is like translating our clues from English into the language of mathematics. The equations will help us organize the information and solve for the unknowns. So, let's get started with setting up these equations!

Equation 1: Sutopa and Maneet

Let's start with the first clue: Sutopa has 34\frac{3}{4} of the money Maneet has. We can write this as an equation: S = 34\frac{3}{4}M. This equation is super important because it directly relates Sutopa's money to Maneet's money. It's like a mathematical way of saying the same thing as the clue. In this equation, S represents the amount of money Sutopa has, and M represents the amount of money Maneet has. The 34\frac{3}{4} tells us the fraction of Maneet's money that Sutopa has. This equation is a key piece of the puzzle because it allows us to express Sutopa's money in terms of Maneet's money. This will be useful later when we need to solve for the unknowns. Remember, this equation is a direct translation of the first clue into mathematical language. It's a foundational equation that we'll use to solve the problem. So, let's keep this equation in mind as we move forward.

Equation 2: Maneet and Kim

Next, let's look at the second clue: Maneet has $18 less than Kim. We can write this as an equation: M = K - $18. This equation tells us how Maneet's money relates to Kim's money. It's a direct comparison in terms of a dollar amount. In this equation, M represents the amount of money Maneet has, and K represents the amount of money Kim has. The "- $18" tells us that Maneet has $18 less than Kim. This equation is crucial because it allows us to express Maneet's money in terms of Kim's money. This is another key piece of the puzzle that we need to solve the problem. This equation is a straightforward translation of the second clue into mathematical terms. It's a simple subtraction that helps us link Maneet's money to Kim's money. So, let's keep this equation handy as we continue to solve the problem.

Equation 3: The Total

Now, let's use the third clue: Together, they have $286.40. We can write this as an equation: S + M + K = $286.40. This equation represents the total amount of money that Sutopa, Maneet, and Kim have combined. It's a comprehensive equation that includes all three people. In this equation, S represents the amount of money Sutopa has, M represents the amount of money Maneet has, and K represents the amount of money Kim has. The "$286.40" is the total amount they have together. This equation is essential because it ties all three people together in one equation. This is the glue that holds all the pieces of the puzzle together. This equation is a direct representation of the third clue in mathematical terms. It's a simple addition that helps us relate the individual amounts to the total amount. So, let's keep this equation in mind as we move towards finding the solution.

Solving the Equations

Alright, we've got our equations set up! Now comes the exciting part: solving them. We have three equations and three unknowns (S, M, and K), which means we can definitely find the solution. The strategy here is to use substitution to eliminate variables and solve for one variable at a time. This might sound a bit technical, but it's like solving a puzzle one step at a time. We'll start by substituting one equation into another to reduce the number of variables. This will help us simplify the problem and get closer to the answer. So, let's dive in and start solving these equations!

Step 1: Substitution

So, in this first step, we're going to use substitution to simplify our equations. Remember our equations? We have S = 34\frac{3}{4}M and M = K - $18. We can substitute the second equation into the first equation. This means we'll replace M in the first equation with (K - $18). This gives us a new equation: S = 34\frac{3}{4}(K - $18). This substitution is super helpful because it allows us to express S in terms of K. Now, we have S in terms of K and M in terms of K. This means we can substitute both S and M in the third equation (S + M + K = $286.40) with expressions involving K. This is a key step in solving the problem because it reduces the number of variables in our main equation. By substituting, we're making the problem easier to solve. It's like simplifying a complex puzzle into smaller, more manageable pieces. So, let's keep this new equation in mind as we move to the next step.

Step 2: Simplify and Solve for K

Now that we've done some substitution, let's simplify and solve for K. We have the equation S + M + K = $286.40, and we know that S = 34\frac{3}{4}(K - $18) and M = K - $18. Let's substitute these into the equation: 34\frac{3}{4}(K - $18) + (K - $18) + K = $286.40. This looks a bit complex, but don't worry, we'll simplify it step by step. First, let's distribute the 34\frac{3}{4}: 34\frac{3}{4}K - 34\frac{3}{4} * $18 + K - $18 + K = $286.40. Now, let's simplify the multiplication: 34\frac{3}{4}K - $13.50 + K - $18 + K = $286.40. Next, let's combine the K terms: 34\frac{3}{4}K + K + K = 2.75K. And let's combine the constants: - $13.50 - $18 = - $31.50. So, our equation becomes: 2.75K - $31.50 = $286.40. Now, let's isolate the K term by adding $31.50 to both sides: 2.75K = $317.90. Finally, let's solve for K by dividing both sides by 2.75: K = $317.90 / 2.75 = $115.60. So, Kim has $115.60! This is a major breakthrough because we've found the amount of money Kim has. This is a crucial step in solving the problem, and we're one step closer to finding the amounts for Sutopa and Maneet. Now that we know K, we can use the other equations to find M and S. So, let's move on to the next step and find out how much money Maneet and Sutopa have.

Step 3: Find M and S

Now that we know Kim has $115.60 (K = $115.60), we can easily find out how much Maneet and Sutopa have. Let's start with Maneet. We know that M = K - $18, so M = $115.60 - $18 = $97.60. So, Maneet has $97.60! This is great progress because we've found the amount of money Maneet has. Now, let's find out how much Sutopa has. We know that S = 34\frac{3}{4}M, so S = 34\frac{3}{4} * $97.60 = $73.20. So, Sutopa has $73.20! This is the final piece of the puzzle. We've found the amounts of money for all three people. We've successfully solved the problem! Now, let's summarize our findings and make sure our solution makes sense.

The Final Answer

Okay, guys, we did it! We've solved the problem and found out how much money each person has. Let's recap our findings:

  • Maneet has $97.60.
  • Sutopa has $73.20.
  • Kim has $115.60.

This is the complete solution to the problem. We've answered the question of how much money each person has. To make sure our solution is correct, let's add up the amounts to see if they equal the total amount given in the problem: $73.20 + $97.60 + $115.60 = $286.40. This matches the total amount, so we know our solution is correct! We've successfully solved the problem and found the amounts of money for Sutopa, Maneet, and Kim. Great job, everyone!

Checking Our Work

It's always a good idea to double-check our work to make sure we didn't make any mistakes along the way. So, let's go through the steps again and make sure everything makes sense. We started with the clues, set up the equations, solved for K, and then found M and S. We also added up the amounts to make sure they equal the total amount. Everything checks out! This is super important because it gives us confidence in our solution. Checking our work is a crucial step in problem-solving. It helps us catch any errors and ensures that our answer is correct. So, always remember to double-check your work, especially in math problems. It's a great habit that will help you succeed in math and in life!

Conclusion

So, guys, we've successfully solved a tricky math problem! We figured out how much money Sutopa, Maneet, and Kim each have by breaking down the problem into smaller steps, setting up equations, and solving them using substitution. We also checked our work to make sure our solution is correct. This is a fantastic achievement! Solving math problems like this can be challenging, but it's also very rewarding. It helps us develop our problem-solving skills, which are valuable in many areas of life. Remember, the key to solving complex problems is to break them down into smaller, more manageable steps. And always double-check your work to make sure you didn't make any mistakes. Keep practicing, and you'll become a math whiz in no time!

I hope you enjoyed solving this problem with me! If you have any questions or want to try another problem, let me know. Keep up the great work, and I'll see you next time!