Orange Math: Solve Stephen's Sales Puzzle!

Let's dive into this juicy math problem involving Mr. Stephen and his oranges! We're going to break it down step-by-step, so it's super easy to follow. Get ready to put on your thinking caps, guys, because we're about to solve this orange mystery!

Understanding the Problem

So, here’s the deal: Mr. Stephen started with a bunch of oranges. He sold 4/9 of them on Saturday morning, then 3/5 of what was left on Saturday afternoon. By the end of Sunday, he sold another 1/2 of his remaining oranges and ended up with 63 oranges. The big question is: How many oranges did Mr. Stephen have at the very beginning?

It sounds a bit complicated, right? But don't worry! We can tackle this by working backward and using some basic fraction skills. The key here is to carefully consider what each fraction represents in relation to the remaining oranges at each stage. We'll use a step-by-step approach to make sure we don't miss anything.

Breaking it Down Step-by-Step

First, let's recap the facts:

• Saturday Morning: Sold 4/9 of the oranges.
• Saturday Afternoon: Sold 3/5 of the remainder.
• Sunday: Sold 1/2 of the remaining oranges.
• End Result: 63 oranges left.

We need to figure out how these fractions relate to each other and, more importantly, how they relate to the final 63 oranges. Remember, fractions represent parts of a whole, and in this case, our “whole” keeps changing as Mr. Stephen sells more oranges. This is a classic problem that involves working backward, a technique often used in algebra and problem-solving.

Working Backwards: Sunday's Sales

Let’s start with the easiest part: Sunday. Mr. Stephen sold 1/2 of his oranges and was left with 63. This means those 63 oranges represent the other 1/2. If 63 oranges are half, then the total number of oranges before Sunday's sales must have been double that amount. So, before Sunday, Mr. Stephen had:

63 oranges * 2 = 126 oranges

See? We've already made progress! We know that Mr. Stephen had 126 oranges at the start of Sunday. This is a crucial piece of the puzzle, so let's hold on to that information. The concept of working backward is extremely useful in many mathematical problems, and here, it allows us to undo the sales one step at a time.

Untangling Saturday Afternoon: The 3/5 Sale

Now, let’s rewind to Saturday afternoon. Mr. Stephen sold 3/5 of his oranges at this point. But 3/5 of what? It's 3/5 of the oranges he had remaining after the morning sales. We know he had 126 oranges before Sunday, and this was after the Saturday afternoon sale. This means the 126 oranges represent what's left after selling 3/5. So, what fraction of the oranges remained?

If he sold 3/5, then he had 1 - 3/5 = 2/5 of his oranges left. This means the 126 oranges represent 2/5 of the oranges he had before the Saturday afternoon sale. To find the total number of oranges he had before this sale, we need to figure out what 1/5 would be, and then multiply that by 5.

First, we divide 126 by 2 to find out what 1/5 is:

126 oranges / 2 = 63 oranges (This represents 1/5)

Now, multiply that by 5 to find the whole (5/5):

63 oranges * 5 = 315 oranges

Awesome! Mr. Stephen had 315 oranges before his Saturday afternoon sales. We're getting closer to the initial number! The method we're using here, of finding the value of a unit fraction (1/5 in this case) and then scaling it up, is a fundamental skill in fraction problems.

Unraveling Saturday Morning: The Initial Amount

Finally, let’s go back to Saturday morning. Mr. Stephen sold 4/9 of his total oranges then. The 315 oranges we just calculated represent what was left after this sale. So, these 315 oranges represent 1 - 4/9 = 5/9 of his original amount. We’re going to use the same technique as before.

First, find out what 1/9 represents by dividing 315 by 5:

315 oranges / 5 = 63 oranges (This represents 1/9)

Now, multiply by 9 to find the total number of oranges (9/9):

63 oranges * 9 = 567 oranges

The Grand Finale: How Many Oranges Did Stephen Initially Have?

We did it! We’ve worked our way back through the sales, step by step. The initial number of oranges Mr. Stephen had was 567.

Therefore, Mr. Stephen initially had 567 oranges.

That was quite a journey, wasn't it? But by breaking the problem down into smaller, manageable steps, we were able to solve it. The strategy of working backward, combined with our understanding of fractions, helped us unravel the mystery of the oranges.

Key Takeaways and Tips

• Read Carefully: Make sure you understand what the problem is asking. Identify the key information and what you need to find.
• Work Backwards: When the problem involves a series of actions, working backward can often simplify the solution.
• Fractions are Your Friends: Understand what each fraction represents in the context of the problem. Remember the “whole” can change! This is super important.
• Step-by-Step: Break down complex problems into smaller steps. This makes the process less overwhelming and easier to follow.
• Check Your Work: If possible, plug your answer back into the problem to make sure it makes sense. You can quickly verify your solution using this approach.

Practice Makes Perfect

Math problems like this can seem daunting at first, but with practice, you’ll become a pro at solving them. Try finding similar problems online or in textbooks and work through them using the techniques we discussed. The more you practice, the more confident you’ll become. Don't be afraid to make mistakes – they are part of the learning process! Each attempt brings you closer to mastery.

Real-World Applications of Fraction Problems

You might be wondering,