23. Exchange Rates
Exchange Rates: Introduction
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Alright. So let's try this example together. But before we get into it, I want to teach you a little trick about exchange rates that comes into play with any kind of unit conversion. So let's do a simple example before we get to this one, where we're going to think about we have we know our exchange of feet to inches, right? We know that there are 12 inches per foot, right? Per 1 foot, which is the same thing as for every 1 foot, there's 12 inches, right? So if I were to ask you, how many inches are in 3 feet? Well, you would probably know that there's 36 inches right? 12 inches per 1 foot, 3 feet, 36 inches right? Well, how do we use this and show it mathematically? Okay. So this is technically our exchange rate here. 12 inches for every 1 foot or 1 foot for every 12 inches right? And we want to know 3 feet, how many inches, right? 3 feet, how many inches? So the idea is we're going to use our exchange rate from inches to feet and we're going to multiply it by feet. Okay? The idea is that we want to end up with inches, right? Our question is asking us, how many inches for in 3 feet? How many inches in 3 feet? So we want to cancel out the units of feet and be left with inches. Let me show you what I mean. So we're going to use our exchange rate, 12 inches for 1 foot and we're gonna multiply it by how many feet we want. We want 3 feet. So in 3 feet, how many inches are there? And what can happen here is we can cancel out these units. So notice that the feet is in the numerator here because it's 3 over 1, right? There's 3 and then there's feet in the denominator. So from a mathematical standpoint, we can cancel out those units, the feet and the feet and we'll be left with inches. This is the way I want you to think about doing these currency exchanges when you have to do math like we see in this problem. So 12 divided by 1 times 3. So now we use the numbers. We've canceled out the units and we're left with inches. 12 divided by 1 is 12 times 3 is 36 inches right? So that tells us that in 3 feet, there's 36 inches right? If there's 12 inches per foot, 3 feet, well, that gets us to 36 inches So what you want to do is be able to cancel out the feet. Notice, if we had used this one right here, 1 foot divided by 12 inches we would not be able to cancel out because feet would have both been in the numerator. We want to cancel out feet and feet here. So this does not work. We want to use this one right here. Okay? So you want to think, we can always flip the exchange rate so that we can cancel out the units that we don't want and end up in the units we do want. Okay? So now let's look at our actual example here. Clutchtopia's currency conversion is currently 1.7 Clutch coin for 1 US dollar. 1.7 Clutch coin cc's per 1 US dollar. So there's our exchange rate. If a US citizen was planning to visit Clutchtopia, how many dollars? So let me erase this right here. How many dollars would they need, right? How many dollars? So we want our final answer to be in dollars, right? So we want to cancel out the clutch coins and be left with dollars. How many dollars would they need to exchange to receive 100 clutch Coins? So what we need to do is convert these units from Clutch Coins to dollars. And we're given our 2 exchange rates here. So I don't want to leave this empty. This was what it was over here before. What are our 2 exchange rates that are equivalent to each other? We either have 1.7 clutch coin per 1 US dollar or 1 US dollar per 1.7 clutch coin. And we want to do the same thing. Do we want to end up in dollars or do we want to end up in clutch coin? What is our question asking us? It's asking us how many dollars, right? So we want to end up in dollars, we want to cancel out the clutch coin. So what we need is clutch coin in the denominator and clutch coin in the numerator to cancel out. Just like we had in our example over here. So what are we going to do? We're going to use this one that has clutch coin in the denominator because we're going to multiply it by a 100 clutch coin. We want to know how many dollars are needed to receive a 100 clutch coins, so we want to go in the bank with a certain amount of dollars and then leave the bank with a 100 clutch coin. So how many dollars is that? So what we're going to do, we're going to do the one one US dollar divided by 1.7 clutch coin and we're gonna multiply it by the 100 clutch coin. Right? We multiply it by 100 because this exchange rate is equal to 1. That's what one would be. So we multiply it by the 100 clutch coins and we'll see how many dollars it would be. So notice what happens. We've got clutch coin in the denominator, clutch coin in the numerator and the clutch coins are gone and we're left with US dollars. So what we need to do is 1 divided by 1.7, so now we do the math. 1 divided by 1.7 times 100 and that gives us that equals 58.82, 58.82 and that's in dollars, right? That gives us an amount in dollars because we've canceled out these clutch coins here and we're left with US dollars. Okay? So that's what this tells us here. It tells us the amount of US dollars we need to get a 100 clutch coins. Okay? So I know it can be a little tricky when it comes to exchange rates, but being able to do this unit conversion and flipping the exchange rate when you need to to cancel out the units, that's a big trick in being able to solve these exchange rate problems. Alright? Let's pause here and now you guys can try a practice sim
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