Marzhan's Shopping Spree: Lottery Tickets, Stamps, And No Change!

Hey guys! Let's help Marzhan figure out how much money she needs to take to the kiosk. This is a classic word problem that involves a little bit of algebra and a whole lot of common sense. The key is to understand that Marzhan needs enough money to buy either lottery tickets or stamps, and since the vendor won't have any change, she needs to bring the exact amount. So, we need to think about the possible scenarios and figure out the worst-case scenario where she needs the most money. Let's break it down step by step, shall we?

Understanding the Problem: The Core of the Matter

First off, let's make sure we really get what's going on. Marzhan is going to the kiosk to buy either lottery tickets or stamps. The lottery tickets cost 80 tenge each, and the stamps cost 60 tenge each. The tricky part? The vendor has no change. This means Marzhan can't just hand over a larger bill and get some money back. She needs to have the exact amount of money ready.

The question is: how much money should Marzhan take from home? Since we don't know exactly how many tickets or stamps she wants (or even if she wants both!), we need to figure out the maximum amount she might need to spend. This is the amount she'll have to take with her to be absolutely sure she can make her purchases. Think of it like this: if she has enough for the most expensive possible purchase, she's covered for everything else too. This problem is all about finding the least common multiple to determine the possible amounts she can spend. Knowing this, let's explore the solutions.

Now, let's explore all of the possibilities. Since the problem doesn't specify how many tickets or stamps Marzhan wants, she could buy any combination of the two. However, we're not given that information. To solve this, we need to think about the multiples of 60 and 80. Since she needs the exact amount, she has to pay in multiples of 60 or 80. Let's see how much she would spend if she wanted the most expensive of one item.

Analyzing the Options: Tickets, Stamps, or Both?

Lottery Tickets Only

If Marzhan only wants to buy lottery tickets, she needs to have enough money to pay for the tickets without receiving any change. Since each ticket costs 80 tenge, she'll need to bring an amount that is a multiple of 80. This could be 80 tenge (for one ticket), 160 tenge (for two tickets), 240 tenge (for three tickets), and so on. Remember, there's no limit on the number of tickets, and therefore, the amount she would need can be 80 times any whole number.

Stamps Only

Alternatively, Marzhan might only want to buy stamps. In this case, each stamp costs 60 tenge, and she needs to bring an amount that's a multiple of 60. So, she could bring 60 tenge (for one stamp), 120 tenge (for two stamps), 180 tenge (for three stamps), etc. As with the tickets, the amount needed is a multiple of the item's cost.

Tickets and Stamps

What if she wants both? This complicates things a bit, but we can still figure it out. She'll need to have enough money for a combination of tickets and stamps. This is where it gets interesting because Marzhan needs to have the ability to pay the exact amount. Imagine if she wants one lottery ticket (80 tenge) and one stamp (60 tenge). She needs 80 + 60 = 140 tenge. The sum of the expenses becomes important. She could also buy two tickets (160 tenge) and one stamp (60 tenge), costing a total of 220 tenge. Thus, she would need to bring a sum that is a multiple of both 60 and 80.

Finding the Solution: The Maximum Possible Amount

To ensure she can buy anything she wants, and because the vendor has no change, we need to find the amount that covers the highest potential cost. Since the tickets and stamps do not have any constraints, it's not possible to determine how much money she needs, unless a constraint is set. We can only conclude that she needs to have the multiple of either 60 or 80 to make the purchase, and if she wishes to buy both, the amount must be the sum of those two. Let's consider some scenarios:

• Scenario 1: Only Lottery Tickets. Marzhan can buy a multiple of 80 tenge.
• Scenario 2: Only Stamps. Marzhan can buy a multiple of 60 tenge.
• Scenario 3: Lottery Tickets and Stamps. Marzhan needs a sum of the multiples of 80 and 60, i.e. 80x + 60y, where x and y represent the number of lottery tickets and stamps respectively. Without further constraints, we can not determine a specific amount.

Since the problem doesn't give us the specific number of tickets or stamps, we can only infer the amount Marzhan needs to take. If she wants to buy only one item, she should take the amount required. If she wants to buy both, she should take the sum.

Conclusion: Packing Marzhan's Wallet

So, guys, what's the takeaway? We've explored the different possibilities, understanding that Marzhan needs to have the exact amount of money to make her purchase due to the lack of change from the vendor. This problem highlights the importance of understanding multiples and thinking about the worst-case scenario. However, without additional information, it is not possible to determine the exact amount Marzhan needs to bring. She must bring a multiple of 80 or 60, or a sum of both if she needs to buy both.

I hope this breakdown was helpful! Feel free to ask if you have any more questions about this problem or any other math puzzles. Keep practicing, and you'll become a word problem whiz in no time!