Cookie Conundrum: Solving Hana's Eid Treat Costs!

Hey guys! Let's dive into a fun math problem about Hana and her Eid cookie shopping. This is a classic algebra problem disguised as a yummy treat scenario. We'll break it down step-by-step so it's super easy to follow. Ready? Let's get started!

Understanding the Problem

So, the core of the problem revolves around figuring out the individual prices of nastar and cheese cookies. The key information we have is:

• One can of nastar cookies costs twice as much as one can of cheese cookies.
• Three cans of nastar cookies and two cans of cheese cookies cost Rp480,000 in total.

Our mission, should we choose to accept it (and we totally do!), is to find out how much Hana needs to pay for two cans of nastar and three cans of cheese cookies. This involves setting up some equations and solving for the unknowns. Think of it like being a detective, but instead of solving a crime, we're solving for cookie prices! It might sound intimidating, but trust me, it's all about breaking it down into smaller, manageable steps.

We can use variables to represent the unknowns. Let's say the price of one can of cheese cookies is "x." Since the price of one can of nastar cookies is twice the price of cheese cookies, we can represent the price of nastar cookies as "2x." This way, we can easily relate the prices of the two types of cookies. Now, we can express the total cost of 3 cans of nastar cookies and 2 cans of cheese cookies in terms of x.

Here is the equation:

3(2x) + 2(x) = 480,000.

Simplifying this equation will allow us to solve for x, which represents the price of one can of cheese cookies. Once we know the value of x, we can easily calculate the price of one can of nastar cookies (2x). With these individual prices in hand, we can determine the total cost of 2 cans of nastar cookies and 3 cans of cheese cookies. This is the final step in solving the problem and finding out how much Hana needs to pay.

Setting Up the Equations

Alright, let's translate the word problem into mathematical equations. This is where the algebra magic happens!

• Let the price of one can of cheese cookies be x.
• Then, the price of one can of nastar cookies is 2x (because it's twice the price of cheese cookies).

Now, let's use the information about the total cost of the cookies:

• 3 cans of nastar cookies cost 3 * (2x) = 6x
• 2 cans of cheese cookies cost 2 * x = 2x

The total cost equation is therefore: 6x + 2x = 480,000.

So, remember how we defined our variables? That's super important. x represents the price of a can of cheese cookies, and 2x represents the price of a can of nastar cookies. Keeping these definitions clear will prevent confusion as we work through the problem. Once we've set up our equation, it's time to combine like terms. In this case, we have 6x and 2x on the left side of the equation. Adding these together gives us 8x. So, our simplified equation is 8x = 480,000. Now, we just need to isolate x to find the price of a can of cheese cookies. To do this, we divide both sides of the equation by 8. This gives us x = 60,000. Therefore, the price of a can of cheese cookies is Rp60,000.

Solving for x

Time to solve for x! We have the equation:

6x + 2x = 480,000

Combine the x terms:

8x = 480,000

Now, divide both sides by 8 to isolate x:

x = 480,000 / 8

x = 60,000

So, what does this mean? It means that the price of one can of cheese cookies (x) is Rp60,000. Yay, we solved for x! But we're not done yet. We still need to find the price of the nastar cookies and then figure out the final cost.

Finding the Price of Nastar Cookies

Now that we know the price of cheese cookies, finding the price of nastar cookies is a piece of cake (or should I say, a piece of kue!). Remember that one can of nastar cookies costs twice as much as one can of cheese cookies. We already found that one can of cheese cookies costs Rp60,000. So, to find the price of one can of nastar cookies, we simply multiply the price of cheese cookies by 2. This gives us 2 * Rp60,000 = Rp120,000. So, one can of nastar cookies costs Rp120,000.

Calculating the Final Cost

Okay, we're in the home stretch! We know:

• One can of nastar cookies costs Rp120,000
• One can of cheese cookies costs Rp60,000

Hana wants to buy 2 cans of nastar cookies and 3 cans of cheese cookies. So, let's calculate the cost of each:

• 2 cans of nastar cookies cost 2 * Rp120,000 = Rp240,000
• 3 cans of cheese cookies cost 3 * Rp60,000 = Rp180,000

To find the total cost, we add these two amounts together:

Total cost = Rp240,000 + Rp180,000 = Rp420,000

Therefore, Hana needs to pay Rp420,000 for 2 cans of nastar cookies and 3 cans of cheese cookies. Awesome! We've successfully solved the problem and found the answer. Now, Hana can confidently go ahead and buy her cookies for Eid.

Answer

The amount Hana has to pay for 2 cans of nastar cookies and 3 cans of cheese cookies is Rp420,000.

Conclusion

So there you have it! We successfully navigated Hana's cookie shopping trip using a bit of algebra. Remember, word problems might seem tricky at first, but breaking them down into smaller steps makes them much easier to solve. Keep practicing, and you'll become a math whiz in no time! And hey, maybe treat yourself to some cookies afterward – you deserve it!