Hey everyone! Let's dive into a fun math problem that involves figuring out Hafiz's score based on the marks obtained by Su Lin and Daud. It's like a little puzzle, and we're going to break it down step by step. So, grab your thinking caps, and let's get started!
Understanding the Problem
In this mathematical challenge, the core of the problem lies in deciphering the relationships between the scores of three individuals: Su Lin, Daud, and Hafiz, so we have to decode the clues to find the final answer. The information we have is:
- Su Lin's marks are double those of Daud.
- The combined marks of Su Lin and Daud amount to 3k.
- Hafiz scores 10 marks more than Su Lin.
Our mission, should we choose to accept it (and we do!), is to express Hafiz's marks in terms of k. This means we need to find an equation or expression where Hafiz's score is equal to something involving the variable 'k'. It sounds a bit like detective work, doesn't it? We need to carefully analyze the clues and piece them together to reveal the final answer.
Setting Up the Equations
The first step in tackling any math problem, especially one like this, is to translate the words into mathematical expressions. It's like turning a sentence into a secret code that only we, as math sleuths, can understand. Let's break down each piece of information:
- "Su Lin obtains double the marks of Daud" can be written as: Su Lin = 2 * Daud. This is our first equation, and it tells us the direct relationship between Su Lin's and Daud's scores. If Daud scored 10 marks, Su Lin scored 20, and so on.
- "Their total marks are 3k" gives us: Su Lin + Daud = 3k. This is crucial because it introduces 'k' into the mix, which is what we ultimately need to relate Hafiz's score to. The total of their scores is represented by 3k, a multiple of 'k'.
- "Hafiz obtains 10 marks more than Su Lin" translates to: Hafiz = Su Lin + 10. This is the final piece of the puzzle, linking Hafiz's score to Su Lin's. We know Hafiz scored 10 more than Su Lin, which means once we know Su Lin's score, we can easily find Hafiz's.
Now we have a system of three equations. Think of it as a network of interconnected clues. To solve for Hafiz's score in terms of k, we need to navigate this network, substituting and simplifying until we isolate Hafiz on one side of an equation. This might sound intimidating, but we'll take it one step at a time, just like any good detective would.
Solving for Su Lin and Daud's Marks
Now that we have our equations set up, the next step is to solve for Su Lin and Daud's individual marks in terms of 'k'. This is like cracking the first level of a puzzle – once we know their scores, we can move closer to finding Hafiz's.
We have two equations involving Su Lin and Daud: Su Lin = 2 * Daud and Su Lin + Daud = 3k. To solve these, we can use a method called substitution. It's like replacing one ingredient in a recipe with another that has the same value.
Since we know Su Lin = 2 * Daud, we can substitute '2 * Daud' for 'Su Lin' in the second equation. This gives us:
2 * Daud + Daud = 3k
Now we have an equation with only one variable, Daud. We can simplify this by combining the terms with Daud:
3 * Daud = 3k
To isolate Daud, we divide both sides of the equation by 3:
Daud = k
Great! We've found that Daud's score is simply 'k'. Now that we know Daud's score, we can easily find Su Lin's score using the first equation, Su Lin = 2 * Daud:
Su Lin = 2 * k
So, Su Lin's score is 2k. We've successfully solved for both Su Lin and Daud's marks in terms of k. This is a significant step forward – we're one step closer to figuring out Hafiz's score!
Calculating Hafiz's Marks
With Su Lin's score determined, calculating Hafiz's marks becomes straightforward. Remember, we have the equation: Hafiz = Su Lin + 10. We've already found that Su Lin's score is 2k.
Now, we simply substitute Su Lin's score (2k) into the equation for Hafiz's marks:
Hafiz = 2k + 10
And there you have it! We've successfully expressed Hafiz's marks in terms of k. Hafiz scored 2k + 10 marks. This means that Hafiz's score is 10 marks more than double the value of k. If k were 50, for example, Hafiz would have scored 2 * 50 + 10 = 110 marks.
This completes our mathematical journey. We started with a set of clues, translated them into equations, solved for the unknowns, and ultimately found the expression for Hafiz's marks. It's like completing a puzzle – each step built upon the previous one, leading us to the final solution. And the satisfaction of cracking the code is a reward in itself!
Conclusion
In conclusion, by carefully analyzing the given information and using algebraic techniques, we were able to determine that Hafiz's marks can be expressed as 2k + 10. The key takeaway here is the power of translating word problems into mathematical equations and then using those equations to solve for unknowns. This is a fundamental skill in mathematics and problem-solving in general.
Remember, math isn't just about numbers; it's about logic, reasoning, and problem-solving. By breaking down complex problems into smaller, manageable steps, we can tackle even the trickiest challenges. So, keep practicing, keep exploring, and most importantly, keep having fun with math! You've got this!