Malik's Equation Error: Finding The Correct Solution

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Hey guys! Today, we're diving deep into a math problem presented by Malik, focusing on solving the equation 25x−4y=10\frac{2}{5}x - 4y = 10 when x=60x = 60. We'll break down Malik's approach, identify any potential hiccups, and ensure we grasp the correct solution. Math can seem daunting sometimes, but don't sweat it! We'll tackle this together, step by step, making sure everything is crystal clear. Understanding the nuances of algebra is super important, not just for exams but for real-world problem-solving too. So, let's get started and unravel this equation!

Malik's solution unfolds as follows:

  1. Original Equation: 25x−4y=10\frac{2}{5}x - 4y = 10
  2. Substitution: 25x−4(60)=10\frac{2}{5}x - 4(60) = 10
  3. Multiplication: 25x−240=10\frac{2}{5}x - 240 = 10
  4. Addition: 25x−240+240=10+240\frac{2}{5}x - 240 + 240 = 10 + 240
  5. Multiplication by Inverse: $\frac{5}{2}[\frac{2}{5}...

Alright, let's dissect Malik's solution step by step to pinpoint exactly where things might have gone sideways. This isn't about pointing fingers, but rather about learning and ensuring we nail the correct methodology. So, let's put on our detective hats and get to work!

Step 1: Original Equation

  • The starting point is the equation 25x−4y=10\frac{2}{5}x - 4y = 10. This is our foundation, and it looks solid. We've got a linear equation with two variables, x and y. No problems here, guys!

Step 2: Substitution

  • Malik substitutes x = 60 into the equation, which is the correct initial move. This gives us 25(60)−4y=10\frac{2}{5}(60) - 4y = 10. Remember, substitution is key in solving many algebraic problems. By replacing x with its given value, we're one step closer to isolating y. This step is crucial, and Malik's nailed it so far!

Step 3: Multiplication (Initial Calculation)

  • Here's where things get interesting. Malik seems to have skipped a calculation step and directly written 25x−240=10\frac{2}{5}x - 240 = 10. But wait a minute! Before we can subtract 240, we need to evaluate 25(60)\frac{2}{5}(60). Let's do that quickly: 25∗60=24\frac{2}{5} * 60 = 24. So, the equation should actually be 24−4y=1024 - 4y = 10. This missed step is a critical point to note. It's super easy to rush through calculations, but accuracy is paramount, folks!

Step 4: Subtraction Isolation

  • Malik's next move seems to misunderstand the original substitution of x=60x = 60. The equation 25x−240=10\frac{2}{5}x - 240 = 10 is incorrect because the term 25x\frac{2}{5}x should have been simplified after substituting x=60x = 60. This is where the solution starts to veer off course. It's essential to remember the order of operations (PEMDAS/BODMAS) to avoid such errors. Guys, always double-check your calculations!

Step 5: Further Steps (Incomplete)

  • The solution is incomplete, but we can infer that Malik intended to isolate the variable. However, since the previous steps contained an error, any further steps based on this flawed equation will also be incorrect. This highlights the importance of catching errors early in the problem-solving process. A small mistake at the beginning can snowball into a much larger issue down the line. So, always be vigilant and methodical!

The primary error in Malik's solution lies in not correctly evaluating 25(60)\frac{2}{5}(60) after substituting x = 60. Instead of calculating this to be 24, Malik proceeded with an incorrect equation. This led to a flawed solution path. It's a classic example of how a seemingly small oversight can derail an entire problem. Remember, guys, math is like building with Lego bricks – each step needs to be perfectly placed for the final structure to stand tall!

Let's walk through the correct solution to make sure we've got this down pat.

  1. Original Equation: 25x−4y=10\frac{2}{5}x - 4y = 10
  2. Substitution: 25(60)−4y=10\frac{2}{5}(60) - 4y = 10
  3. Simplify: Calculate 25∗60=24\frac{2}{5} * 60 = 24, so the equation becomes 24−4y=1024 - 4y = 10
  4. Isolate the y term: Subtract 24 from both sides: −4y=10−24-4y = 10 - 24, which simplifies to −4y=−14-4y = -14
  5. Solve for y: Divide both sides by -4: y=−14−4y = \frac{-14}{-4}, which simplifies to y=72y = \frac{7}{2} or 3.5

Therefore, the correct solution is y = 3.5. See how each step flows logically, building upon the previous one? That's the beauty of a well-executed math problem!

So, what have we learned from Malik's mathematical journey? A few crucial things:

  • Accuracy in Calculations is Paramount: A small error can lead to a completely wrong answer. Always double-check your calculations, especially in the initial steps.
  • Order of Operations Matters: Remember PEMDAS/BODMAS! Following the correct order ensures you're solving the equation logically.
  • Step-by-Step Approach: Break down the problem into smaller, manageable steps. This makes it easier to spot errors and keeps your solution organized.
  • Don't Rush: Take your time and think through each step. Rushing often leads to mistakes.

We've successfully navigated through Malik's equation, identified the error, and arrived at the correct solution. Remember, guys, math is a journey of learning and discovery. Mistakes are simply opportunities to grow and refine our problem-solving skills. Keep practicing, stay curious, and you'll conquer any mathematical challenge that comes your way! You got this!