Cheapest Way To Buy 18 Cans Of Cola A Mathematical Breakdown

Hey there, math enthusiasts and cola lovers! Ever found yourself staring at the shelves, wondering how to snag the most cans of your favorite fizzy drink without emptying your wallet? Well, today, we're diving deep into a classic problem: figuring out the cheapest way to buy 18 cans of cola. This isn't just about quenching your thirst; it's a fun exercise in mathematical optimization! We'll break down the different deals, crunch the numbers, and unveil the ultimate strategy to save those precious pennies. So, grab a can (or maybe not, until we figure out the best deal!), and let's get started!

Understanding the Deals

Okay, so let's break down the deals we've got on the table. We're presented with three distinct purchasing options, each with its own pricing structure and potential savings. To effectively determine the cheapest method for acquiring 18 cans of cola, we must meticulously analyze each option, considering both the individual cost per can and the bulk discounts offered. This initial step is crucial in laying the groundwork for our comparative analysis, allowing us to identify the most economical path to cola nirvana. Let's dive into the specifics, shall we?

Single Cans: The Individual Route

The first option, the single can purchase, presents a straightforward pricing model: each can costs 70p, with a tantalizing twist – a "Buy 2 get 1 free" offer. This seemingly simple promotion introduces a layer of complexity to our calculations, as the effective price per can fluctuates depending on the quantity purchased. At first glance, buying single cans might appear to be the most expensive route, especially when compared to bulk pack options. However, the "Buy 2 get 1 free" deal throws a wrench into that assumption, potentially making this option more competitive than initially perceived. To accurately assess its cost-effectiveness, we need to determine the actual price per can when factoring in the free cans. Specifically, for every three cans purchased, only two are paid for, altering the overall cost structure. This requires a bit of arithmetic finesse to unravel, but fear not, we're up for the challenge!

To truly understand the implications of this deal, let's consider how it impacts the cost of acquiring our target of 18 cans. We need to figure out how many sets of three cans we'd need to purchase, and how many of those cans would be free. This will give us a clearer picture of the total cost associated with this option, and allow us to compare it fairly against the other available deals. So, let's sharpen our pencils and start crunching those numbers!

Pack of 4: The Mid-Size Option

Next up, we have the pack of 4, priced at £2.40 per pack, with an additional incentive: purchase two packs, and the price drops to £4. This mid-size option offers a blend of convenience and potential savings, sitting between the individual can purchase and the larger pack of 12. The pricing structure here is slightly more complex than the single can option, as the price per can varies depending on whether you buy one pack or two. Purchasing a single pack of 4 works out to a certain price per can, but buying two packs unlocks a lower price point, thanks to the bulk discount. This tiered pricing system adds another layer of strategic thinking to our quest for the cheapest cola.

To fully evaluate the pack of 4 option, we need to consider how many packs we would need to buy to reach our target of 18 cans. Since 18 isn't a multiple of 4, we'll likely need to purchase a combination of single packs and the discounted two-pack deal to reach our goal. This means carefully weighing the cost of buying individual packs versus the savings offered by the two-pack promotion. It's a balancing act, but with a little mathematical maneuvering, we can determine the most economical approach within this option. We'll need to explore different scenarios, such as buying four packs and then subtracting cans, or buying a certain number of two-pack deals and supplementing with individual packs. Each scenario will have a different cost associated with it, and our mission is to pinpoint the absolute cheapest one.

Pack of 12: The Bulk Buy

Finally, we arrive at the pack of 12, priced at £5.50 per pack. This is the bulk buy option, appealing to those with a serious cola craving or perhaps a party on the horizon. Buying in bulk often translates to significant savings, and the pack of 12 certainly seems promising in that regard. The pricing is straightforward – a fixed price per pack – which simplifies our calculations somewhat. However, the challenge lies in determining how efficiently this option fits into our goal of acquiring 18 cans. Since 18 isn't a multiple of 12, we'll need to consider the implications of buying more cans than we need, or supplementing a pack of 12 with other options.

To assess the true cost-effectiveness of the pack of 12, we need to evaluate the potential for leftover cans. If we buy two packs of 12, we'll end up with 24 cans, exceeding our target by 6. This raises the question of whether the savings from buying in bulk outweigh the cost of the extra cans. Alternatively, we could buy one pack of 12 and supplement with other options, such as single cans or packs of 4, to reach our target of 18. This hybrid approach requires careful consideration, as we need to balance the bulk discount of the pack of 12 with the potential cost-effectiveness of the other options. It's a puzzle, but a solvable one, and we're determined to find the most economical solution!

Crunching the Numbers: Finding the Cheapest Path

Alright, guys, it's time to put on our mathematician hats and dive into the nitty-gritty of the calculations. We've laid out the deals, now let's see which one will give us the most cola for our cash. This is where the real fun begins – we'll be comparing costs, exploring different scenarios, and ultimately uncovering the cheapest way to snag those 18 cans. Get ready to sharpen your mental math skills, because we're about to embark on a numerical adventure!

Single Cans: The Real Cost

Let's revisit the single cans. At 70p each with a "Buy 2 get 1 free" offer, the math gets interesting. For every three cans, you only pay for two, which means the cost for three cans is 70p * 2 = £1.40. To get 18 cans, you'd need six sets of three cans (18 / 3 = 6). So, the total cost would be £1.40 * 6 = £8.40. This gives us a benchmark to compare against the other options. It's crucial to remember this effective price per can when evaluating the overall cost, as the "Buy 2 get 1 free" offer significantly alters the economics of this option. Without considering this promotion, we might prematurely dismiss the single cans as being too expensive. However, by factoring in the free cans, we gain a more accurate understanding of the true cost.

Now, let's consider the implications of this cost in the context of our 18-can target. We know that buying single cans involves purchasing in sets of three to maximize the benefit of the promotion. This means we'll always be buying a multiple of three cans. In our case, 18 is a multiple of three, so we can perfectly achieve our target without any leftover cans. This is a significant advantage, as we won't be paying for any excess product. The key takeaway here is that the "Buy 2 get 1 free" offer makes the single can option surprisingly competitive, and we need to carefully compare it against the other deals to determine the absolute cheapest solution.

Pack of 4: Multiple Scenarios

Now, let's tackle the pack of 4. Remember, they're £2.40 each, or two packs for £4. To get 18 cans, we could consider a few options:

• Option 1: Four packs of 4 (16 cans) plus two single cans. This would cost (£2.40 * 4) + (70p * 2) = £9.60 + £1.40 = £11.00. Ouch! This option seems quite expensive, as we're essentially paying full price for four packs and then supplementing with individual cans. This highlights the importance of maximizing the bulk discount opportunities to minimize the overall cost.
• Option 2: Two sets of two packs (16 cans) plus two single cans. This costs (£4 * 2) + (70p * 2) = £8.00 + £1.40 = £9.40. This is a slight improvement, but still not ideal. While we're taking advantage of the two-pack discount, we're still incurring the cost of individual cans, which drives up the total price.
• Option 3: Five packs of 4. This gives us 20 cans, which is more than we need, but costs £2.40 * 5 = £12.00. This is the most expensive option, as we're not only buying more cans than necessary but also paying full price for each pack. This scenario clearly demonstrates the inefficiency of buying excess product without leveraging bulk discounts.

As you can see, the pack of 4 option presents a few different paths, each with its own price tag. We've identified the costs associated with these scenarios, and it's becoming clear that this option might not be the most economical route to our 18-can goal. The combination of single packs, two-pack deals, and leftover cans makes this option a bit of a mathematical maze, and so far, the numbers aren't looking particularly favorable. We need to carefully weigh the costs and benefits of each scenario to determine if there's a hidden gem within this option, or if we should focus our attention on the other deals.

Pack of 12: The Big Box Gamble

Let's explore the pack of 12, priced at £5.50. To get 18 cans, we have two main choices:

• Option 1: One pack of 12 plus six single cans. This would cost £5.50 + (70p * 6) = £5.50 + £4.20 = £9.70. This option combines the bulk discount of the pack of 12 with the flexibility of individual cans, allowing us to precisely reach our 18-can target. However, the cost of the six single cans adds a significant expense, which we need to compare against the other options.
• Option 2: Two packs of 12. This gives us 24 cans for £5.50 * 2 = £11.00. While this is cheaper per can, we're buying six extra cans, which might not be ideal. This scenario highlights the classic dilemma of bulk buying: are the savings worth the excess? We need to carefully weigh the cost of the extra cans against the lower price per can to determine if this is a worthwhile strategy.

The pack of 12 presents a clear trade-off: either buy exactly what you need by supplementing with single cans, or buy in bulk and have leftovers. The cheaper per-can price of the two-pack option is enticing, but the cost of the extra cans might outweigh the savings. This is a crucial decision point in our quest for the cheapest cola, and we need to carefully consider our priorities: is it more important to minimize the overall cost, or to avoid buying unnecessary cans? The answer to this question will help guide us towards the optimal solution.

The Verdict: Cheapest Way to 18 Cans

Drumroll, please! After all the calculations, it's time to reveal the cheapest way to buy 18 cans of cola. We've crunched the numbers, weighed the options, and navigated the deals, and now the answer is clear. So, which strategy reigns supreme in the quest for cola cost-effectiveness? Let's find out!

Comparing our results:

• Single cans: £8.40
• Pack of 4: The best option was £9.40
• Pack of 12: The best option was £9.70

It's clear that the **cheapest way to buy 18 cans is by purchasing single cans with the