Solve Ticket Sales: How Many Did Each Sell?

by Chloe Fitzgerald 44 views

Hey guys! Ever find yourself scratching your head over a math problem that seems trickier than it should? Well, today we're diving into a classic scenario: figuring out how many tickets André and his buddy sold when they worked together. It’s one of those problems that looks complex at first glance, but trust me, we're going to break it down step by step so it feels as easy as pie. So, buckle up, and let's get started!

The Ticket-Selling Puzzle

Let's kick things off by stating the problem clearly. André and his friend teamed up for a 3-hour ticket-selling marathon, managing to sell a total of 40 tickets. That’s a solid effort, right? Now, here’s the kicker: André, being the super-seller he is, sold 10 tickets more than his friend did. The big question looming over us is: How many tickets did each of them sell individually? We've got three options laid out for us:

  • A) AndrĂ©: 25, Friend: 15
  • B) AndrĂ©: 20, Friend: 20
  • C) AndrĂ©: 30, Friend: 10

Which one is the right answer? Before we jump to conclusions, let's roll up our sleeves and work through the problem methodically. Math problems like this are all about setting up the right equations and solving them logically. No stress, though! We're in this together, and by the end, you'll be able to tackle similar puzzles with confidence. This type of problem often appears in real-life situations, such as managing sales teams or splitting earnings, so understanding the solution isn't just about the numbers; it's about applying practical math skills.

Laying Down the Mathematical Foundation

Alright, let's translate this ticket-selling saga into the language of math. This is where we get to play with some algebraic expressions to represent what's going on. First things first, we need to assign variables. Let's keep it simple and say:

  • Let x be the number of tickets AndrĂ©'s friend sold.

Since André sold 10 more tickets than his friend, we can express the number of tickets André sold as:

  • André’s tickets = x + 10

Now, we know they sold a combined total of 40 tickets. So, we can set up our main equation by adding the number of tickets each of them sold and setting it equal to the total. This gives us:

  • x + (x + 10) = 40

This equation is the heart of our solution. It captures the essence of the problem in a neat, mathematical form. Once we solve for x, we're halfway to our answer. Remember, the goal here is to find the value of x that makes this equation true. Equations like these are the bread and butter of algebra, and mastering them opens up a whole new world of problem-solving possibilities. Think of it as unlocking a secret code – once you know the key (in this case, how to solve the equation), you can decipher countless similar challenges. So, let's dive into solving this equation and see where it leads us!

Cracking the Code: Solving the Equation

Okay, folks, let’s get our hands dirty and solve this equation. We've got: x + (x + 10) = 40. The first step is to simplify the equation by combining like terms. This just means grouping the x’s together. So, we have:

  • 2x + 10 = 40

Now, our mission is to isolate x on one side of the equation. To do this, we need to get rid of that pesky +10. We can do that by subtracting 10 from both sides of the equation. Remember, what we do to one side, we must do to the other to keep things balanced. This gives us:

  • 2x + 10 - 10 = 40 - 10
  • 2x = 30

We’re almost there! Now, we have 2x = 30. This means 2 times x equals 30. To find x, we need to undo the multiplication. The opposite of multiplication is division, so we'll divide both sides of the equation by 2:

  • 2x / 2 = 30 / 2
  • x = 15

Boom! We’ve solved for x. This tells us that André's friend sold 15 tickets. But hold on, we’re not done yet. We still need to figure out how many tickets André sold. Remember, André sold 10 more tickets than his friend. So, we'll add 10 to the value we found for x.

This process of solving for the unknown is a fundamental skill in mathematics and beyond. Whether you're balancing a budget, planning a project, or even figuring out how long it will take to drive somewhere, the ability to set up and solve equations is incredibly valuable. And the best part? It's all about logical steps, just like we're doing here. So, let's finish this ticket puzzle and celebrate our math prowess!

Unveiling the Ticket Totals

Alright, now that we know André's friend sold 15 tickets (that’s our x), let’s calculate André's sales. Remember, André sold 10 more tickets than his friend, so we just need to add 10 to the number of tickets his friend sold:

  • André’s tickets = x + 10
  • André’s tickets = 15 + 10
  • André’s tickets = 25

So, André sold 25 tickets! Now we have the individual totals: André sold 25 tickets, and his friend sold 15 tickets. Let’s just double-check to make sure our solution makes sense. If we add the number of tickets André sold to the number his friend sold, do we get the total of 40 tickets?

  • 25 + 15 = 40

Yep, it checks out! We’ve successfully cracked the code. The next step is to match our findings with the options we were given at the start. This is a crucial step in problem-solving – always make sure your answer aligns with the options or the context of the problem. It's like having a key that fits the lock perfectly; you want to make sure you're using the right one. And speaking of the right key, let’s see which of our options matches our solution.

The Grand Reveal: Picking the Right Answer

Okay, drumroll, please! We’ve done the math, and we know that André sold 25 tickets and his friend sold 15 tickets. Now, let's revisit the options we had at the beginning and see which one matches our solution:

  • A) AndrĂ©: 25, Friend: 15
  • B) AndrĂ©: 20, Friend: 20
  • C) AndrĂ©: 30, Friend: 10

It’s pretty clear, isn’t it? Option A perfectly aligns with our calculations. André sold 25 tickets, and his friend sold 15 tickets. Woohoo! We nailed it!

Option A is the correct answer. But before we pat ourselves on the back too hard, let’s quickly think about why the other options are incorrect. This is a great way to reinforce our understanding and make sure we’re not just guessing. Option B suggests both André and his friend sold 20 tickets each, which would total 40 tickets, but it doesn't account for the fact that André sold 10 more tickets than his friend. Option C is also close in total numbers but doesn't accurately reflect the 10-ticket difference between André’s sales and his friend’s. By understanding why the incorrect options are wrong, we strengthen our grasp of the problem-solving process.

Final Thoughts on Cracking Math Problems

So, guys, we’ve successfully navigated the ticket-selling problem and found our answer. But more than just finding the right number, we’ve walked through a process that can be applied to countless other math challenges. Remember, it’s all about breaking down the problem, setting up the right equations, and solving them step by step.

Math problems, especially word problems, might seem daunting at first. But think of them as puzzles waiting to be solved. Each piece of information is a clue, and your job is to fit those clues together to reveal the solution. It’s like being a math detective, piecing together the evidence to crack the case. And just like any skill, the more you practice, the better you get. So, don’t shy away from challenges; embrace them as opportunities to grow your problem-solving muscles. And remember, we’re all in this together. Keep practicing, keep questioning, and keep exploring the wonderful world of mathematics!