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Converting Between Celsius and Fahrenheit

Patrick Ford
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Hey guys got a pretty interesting problem here. This is a pretty common one that pops up. We're gonna calculate the one magical temperature where the Celsius and Fahrenheit scales are equal to each other. So if you know anything about the Celsius and Fahrenheit scales, remember that zero degrees Celsius is equal to 32 F, We've seen that before. Another one sort of special number that we saw Is that a 100°C is equal to 212 F. So if you look what's happening here, we grow 100. So you're growing 100 degrees in the Celsius scale, but you're growing 180 degrees in the Fahrenheit scale. So basically what happens is that the Fahrenheit scale grows a little bit faster than the Celsius scale. And what happens is if you work backwards, there's going to be one magical temperature where the two numbers are equal to each other. So basically what that means, if I can sort of put that in terms of variables, is that T. C. Is gonna equal T. F the same number. The number in Celsius is gonna be the same exact number in Fahrenheit. So then how do we solve for this magical number here? We're gonna need an equation that relates these two variables together. So basically what that means is that on our conversion table, we can either be given Celsius or ask for Fahrenheit, which means we'll be using this equation or we can work the other way, we can be given Fahrenheit and asked for Celsius in which we'll use this equation. You just need one equation that relates the Fahrenheit and Celsius scales. So either one of these will work. Now I think this one does a little bit easier because this equation has a parenthesis in it. But just in case you did pick that you can actually just go ahead and get the same answer with that. All right, so let's get started here, basically what this means is that T. F is gonna equal 9/5 T. C plus 32. Now, what happens is I have two variables in here, but I know that these two variables are going to be the same exact number. The whole point of this problem is that we're looking for the one temperature in which these two things are equal to each other. So what I can do is I can just replace both of these variables was just a single T. Just one variable. So what that means is that T is equal to 950 Plus 32. Now, all I have to do is really just solve for this t here, that's the one number in which these two things will be equal to each other. Alright, so really this is just a couple of algebra steps, basically we can do as we have tea on one side and t on the other. I want to subtract this over here but I've got a fraction in here. So what I have to do is I'm gonna do t I'm gonna minus 9/5 off from this side but then I have to move it over to this side. So I have to subtract 9 50 this is going to be 32. Now what happens here? I've got t minus 9 50. And the only way I can subtract these two is if I make the denominator the same, so this is just one T. So I can convert this to a fraction by just saying that this is 5 right? That's the same thing. All I'm doing here is I'm just making these denominators equal to each other. So if you work out with this step is this is just gonna be negative 4 50 equals 32. Now I've just got one last step to do, I just have to divide by this negative 4 50. So I'm gonna divide by negative 4/5 over here and then I have to do the same thing to the other side. And then basically what you end up with, is that a. T. Is equal to negative 40 degrees. So what that means is that negative 40 degrees Celsius is equal to negative 40 F. Now there's one really easy way that you can check for this, This is basically what the answer is all you have to do is just plug in negative into this equation. And then what you'll get here is negative 40. So those two things are going to be equal anyway, so that's it for this one, guys, let me know if you have any questions.
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