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 these Celsius and Fahrenheit scales, remember that 0 degrees Celsius is equal to 32 degrees Fahrenheit. We've seen that before. Another one sort of special number that we saw is that 100 degrees Celsius is equal to 212 degrees Fahrenheit. 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 gonna 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 Tc is gonna equal Tf, 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. Alright? So let's get started here. Basically, what this means is that Tf is gonna equal 9/5 Tc plus 32. Now what happens is I have 2 variables in here, but I know that these two variables are gonna 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 with just a single t, just one variable. So what that means is that t is equal to 9/5 t 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, what we can do is we have t 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, and minus 9/5 off from this side but then I have to move it over to this side. So I have to subtract 9/5 t and this is gonna be 32. Now what happens here, I've got T minus 9/5 T. Now the only way I can subtract these 2 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 5/5 t. 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 this step is this is just gonna be negative 4/5 t equals 32. Now I've just got one last step to do. I just have to divide by this negative 4/5 t. 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 t is equal to negative 40 degrees. So what that means is that negative 40 degrees Celsius is equal to negative 40 degrees Fahrenheit. 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 40 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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