Lucia's Candy Purchase: How Much Change?

Hey guys! Today, we're diving into a fun math problem about Lucia and her sweet tooth. She bought a bunch of goodies, got a sweet discount, and paid with a $200 bill. The big question is: How much change did she get back? Let's break it down step by step so you can follow along easily. Stick with me, and you'll not only solve this problem but also sharpen your math skills for everyday situations. Understanding how to calculate these kinds of transactions is super useful, whether you're buying candy like Lucia or budgeting your own expenses. Ready? Let's get started and figure out Lucia's change together!

Calculating the Cost of Candies

So, Lucia picked up a variety of treats: 2.35 kg of gummies, 1.75 kg of chocolate, and a delightful 0.8 kg of marshmallows. Now, each kilogram of these sugary delights costs $45.60. To figure out the total cost before any discounts, we need to calculate the individual costs and then add them all up. First, let's find out how much the gummies cost. We multiply the weight of the gummies (2.35 kg) by the price per kilogram ($45.60). This gives us the cost of the gummies. Next, we do the same for the chocolate. We multiply the weight of the chocolate (1.75 kg) by the price per kilogram ($45.60) to get the cost of the chocolate. Finally, we calculate the cost of the marshmallows by multiplying their weight (0.8 kg) by the price per kilogram ($45.60). Once we have these three individual costs, we add them together to get the total cost of all the candies before the discount. This is a crucial step, guys, because it sets the stage for figuring out how much Lucia actually paid and how much change she received.

By calculating each sweet separately and then combining the totals, we avoid confusion and ensure accuracy. Think of it like separating your grocery list – you calculate the cost of fruits, vegetables, and snacks individually before adding them all up at the checkout. This method makes the whole process much clearer and easier to manage. It’s also a great way to double-check your calculations and make sure you haven't made any mistakes along the way. So, let’s get those numbers crunched and find out the initial cost of Lucia's candy haul!

Applying the Discount

Lucia is one lucky customer! Because she's a frequent shopper, she gets a discount of $12.50. After we've calculated the total cost of the candies, we need to subtract this discount to find out how much Lucia actually has to pay. To do this, we take the total cost we calculated in the previous step and simply subtract $12.50 from it. This gives us the final amount that Lucia owes the cashier. Discounts are fantastic, aren't they? They help us save money and make our purchases more affordable. In this case, Lucia's frequent shopper discount significantly reduces the amount she has to pay for her sweet treats. Understanding how discounts work is super important in real life, whether it's a percentage off, a fixed amount like Lucia's, or a buy-one-get-one-free deal.

Knowing how to apply these discounts correctly ensures that you're always getting the best possible price. It's also a great way to compare prices and decide where to shop. For example, if two stores sell the same item but one offers a discount, you can easily calculate which store offers the better deal. In Lucia's case, the $12.50 discount is a straightforward subtraction from the total cost. This makes it easy to see the immediate savings she's getting. So, after subtracting the discount, we'll have the exact amount Lucia needs to pay, which will help us determine how much change she receives from her $200 bill. Let's make sure we subtract correctly to get the most accurate result!

Calculating the Change

Okay, so Lucia hands over a $200 bill. Now, we need to figure out how much change she gets back. To do this, we take the amount she paid ($200) and subtract the final cost of the candies after the discount. This difference is the amount of change she receives. It's a simple subtraction problem, but it's super important to get it right! Change calculations are an essential part of everyday life. Whether you're buying groceries, grabbing a coffee, or, like Lucia, indulging in some sweet treats, knowing how to calculate change accurately is crucial. It helps you ensure that you're receiving the correct amount back and prevents any potential errors. This skill is also incredibly useful when you're handling cash in any setting, whether it's at a store, a market, or even just splitting bills with friends.

Understanding the process of calculating change can also give you a better sense of your spending habits. By knowing exactly how much you're spending and how much change you're receiving, you can keep track of your expenses more effectively. This can be especially helpful if you're trying to budget or save money. So, let's make sure we subtract the final cost from $200 correctly to determine exactly how much change Lucia receives. This will complete our sweet adventure and give us the final answer to our math problem. Are you ready to see the result? Let's crunch those numbers one last time and reveal Lucia's change!

Step-by-Step Calculation:

1. Calculate the cost of the gummies: 2.35 kg * $45.60/kg = $107.16
2. Calculate the cost of the chocolate: 1.75 kg * $45.60/kg = $79.80
3. Calculate the cost of the marshmallows: 0.8 kg * $45.60/kg = $36.48
4. Calculate the total cost before the discount: $107.16 + $79.80 + $36.48 = $223.44
5. Apply the discount: $223.44 - $12.50 = $210.94
6. Calculate the change: $200 - $210.94 = -$10.94

Final Answer

Oops! It seems like there was a mistake in the numbers provided. Based on the calculations, the total cost of the items after the discount is $210.94, but Lucia only paid with $200. This means Lucia is short $10.94; in this situation, Lucia did not receive any money, but she needs $10.94 to cover the cost of the items.

I hope this step-by-step breakdown was helpful and easy to follow! Even though the numbers didn't quite add up in this scenario, the process of calculating costs, applying discounts, and figuring out change is super important in everyday life. So, keep practicing those math skills, and you'll be a pro at handling money in no time!