Alright. Let's go ahead and try this one here. So, it gives us a couple of curves here. We've got a supply curve and a demand curve, and it's asking us to find the equilibrium price and quantity. First thing you should notice is that different variables are isolated in each equation, right. In our demand equation, the first equation, price is isolated and in the second equation, the supply equation, quantity is isolated. And how do I know which is which? It's because the first one has quantity demanded in it, the second one has quantity supplied in it, okay? So the first thing we want to do is isolate the same variable. So I don't like the looks of the first equation, I kind of think that fraction is just messing with me. I'm going to rearrange that so that I have quantity supplied or quantity demanded by itself, but remember, you could also rearrange the other one, and we'll get to the same answer. This is the way I'm going to do it.
So we've got p = 6 − 150 QD. Right? And I want to get that QD by itself. So, the first thing we need to do is move that 6 from one side to the other, and we're going to get p − 6 = −150 QD. So how do we get rid of that pesky fraction? We need to multiply by the reciprocal, right? So, I'm going to multiply by 50 over 1, right? So just negative 50, so multiply by negative 50, and negative to get rid of the negative sign in the front there. So I want to do negative times a negative to get rid of the negative, and then the 50 times the 150 to cancel out that fraction.
So if I'm going to multiply this side by negative 50, I need to multiply the other side by negative 50 as well. Let's go ahead and isolate this variable. So, this negative and this negative cancel, the 50 and the 150 cancel, and we're left with just quantity demanded on this side of the equation, and let's expand this out. We've got negative 50 times p, so negative 50
and negative 50 times negative 6. Those negatives are going to cancel out. We're going to get a positive, 6 times 50 is 300. Alright. So, negative 50 times p and then negative 50 times negative 6. So there we go. That is going to be the same equation with quantity demanded isolated. Rights. Now we can go on to the next step where we set the 2 equations equal to each other based on that isolated variable.Alright. So, I'm going to take this side of this equation right here and this side of this equation right here, our supply and our demand equation, and let's go ahead and set them equal. So − 50p + 300 = 150p − 100. Alright, so now I want to isolate my Ps, so I'm going to get them all on one side. Plus 50
plus 50, and I will have 200 over here minus 100, and on this side the ps are canceled, and I'll have 300. 300 equals 200 minus 100. Let's go ahead and add 100 to each side. So 400 equals 200, that cancels. We'll divide both sides by 200, and we'll get an answer of p = 2. Alright, so we've figured out what p is, Now it's just a matter of plugging this into either of our original equations, and we will get our quantity. So, this will be our equilibrium price and based on this alone, we'll know which answer to the question it is, right? It's going to be B. See, only one with an equilibrium price of 2. So on a test, you're crunched for time. Hey, this is enough information to get this right, but let's go ahead and finish it up.So with the price of 2, I'm going to go ahead and use the supply equation. It looks easier to just plug a number in, so quantity supplied or just quantity, right, at equilibrium, they're going to be the same for demand and supply. Quantity equals 150 times our price of 2 minus 100. Right, so I just took this equation up here, QS = 150p − 100, plugged in 2 for p, and let's find out what Q equals. 300, 150 times 2 is 300, minus 100, Q = 200. Just like we see in that answer, so the answer is going to be B. Alright, let's move on.