The supply and demand curves for a product are as follows: Q d = 10560 − 80 P Q_{d}=10560-80P P = 1 40 Q s + 6 P=\frac{1}{40}Q_{s}+6 What is the equilibrium price and quantity of the product?

Alright. Let's tackle this practice problem. The supply and demand curves for a product are as follows and we are given a demand curve there first and a supply curve there second. What is the equilibrium price and quantity of the product? So right away you should notice that we do not have the same variables isolated in each equation right? On the demand equation up here, quantity demanded is by itself. For the supply equation, price is by itself. So our first step is to get the same variable isolated in both equations, and I am going to take the second equation. I don't like this fraction, I wanna get rid of it, and I'm gonna rearrange our supply equation so that quantity supplied is by itself. Alright. And remember if the problem just gave you price by itself here and not quantity demanded, right, then we're good to go. We're ready to go. If you have you know you would have price here and this would be the quantity demanded figure over here or something, then we don't have to do any of this rearranging and we're ready to just set them equal to each other, but this problem gave us tricky different isolated variables so let's go ahead and rearrange this formula right here. So we have p equals 140th qs plus 6. Alright. First step is to get rid of that 6 so we can get the qs by itself. Minus 6, minus 6. P minus 6 equals 1 40th QS. Alright and now to get the QS by itself, we need to get rid of the 1 40th. So we're dividing there by 1 40 so we need to multiply by 40 to get rid of the 1 40th. Multiply by 40 to get rid of the 1 40th. Let me do that in blue. And this side we also have to multiply by 40, right? And everything's getting multiplied by 40 not just the p and not just the 6, the whole side has to get the 40. Okay. So let's go ahead this is gonna cancel with this and we'll be left with just Qs on that side of the equation. Let's expand this out, the 40 times the p is gonna be 40p, and the 40 times the negative 6 is gonna be minus 40 times 6, 240. So 40p minus 240 is gonna equal quantity supplied. So now that we've got quantity supplied isolated here, quantity demanded is isolated over here, we are ready to set them equal to each other. Okay, so I'm gonna set that, what we just solved for equal to this quantity demanded amount over here. So 40p minus 240 equals 10,560 minus 80p. Alright so let's go ahead and add 80p to both sides. This way we stay with positive numbers, it's just easier, And we are gonna get 120p minus 240 equals 10560 and this will cancel. Right? And next we want to add 240 to each side, plus 240 plus 240. Alright. This is gonna cancel and we'll be left with 120p equals 10 800. Right? And let's go ahead and divide both sides by a 120 to get p by itself. Alright, so I can't do this math in my head. I'm gonna need a second let's see, 108100 divided by 120, it's gonna give us a price of 90. Right there. So we figured out our equilibrium price is going to be 90 and if we look at our multiple choice answers, we can see there's only one that says 90 so our work could be done but I want to just double check and that's as easy as taking this 90 and plugging it into one of our original equations. Okay so I'm going to go ahead and pick the first equation, it looks pretty easy, and I'm going to say q equals 105.60 minuteus 80 times our price that we just solved for which was 90, right. So q equals 10560 minuteus 80 times 90 is 7200 and then we just do that math, q equals 10560 minuteus 7200 is 33.60 and that is the quantity that we got there. So we've solved for equilibrium price, equilibrium quantity, the answer here is D. Great. Let's move on.