 This video is going to talk about how to translate applications into algebra and then be able to simplify the expression you make. Our first example, find the perimeter of the Lincoln Memorial Reflecting Pool in Washington, DC. The reflecting pool is approximately 2,029 feet long and 167 feet wide. Well, one of the first things we need to know here is what are we trying to find? And what is perimeter? Well, that's the formula 2L plus 2W. And L, in our case, is how long it is, and that's 2,029. And W, in our case, is how wide it is, so that's 167. So now we just really have to plug and check. We want to find the perimeter, and it's 2 times the length, 2,029, plus 2 times the width, 167. And I'm going to use my calculator over here. So 2, exactly like I see it, parentheses, 2,029, close my parentheses, plus 2, and then parentheses, 167, close the parentheses, and Enter. And that says that that is equal to 4,392, and this would be, perimeter would be feet. It was in feet up here, so that means that's what our perimeter is going to be. Second example, in a rectangle, the width is four less than twice the length. If L represents a length, write an expression that represents the width of the rectangle. So we want to know width is equal to what? And they tell us here that the width is, so that usually means equal, and then they're going to tell us what it is. It's four less than twice the length. And if you remember from translating, when you see that, then we have to switch them. So the four is going to be on this side, and twice the length is going to be this side. So twice the length is actually going to be first. So that's two times the length, and it says up here that L represents the length. So that's 2L. Less than means minus. And then four less than that would be minus four, 2L minus four is what width is equal to. We just needed the expression. All right, at Los Angeles Valley College, it's in state resident tuition and fees for academic year 2010 and 11 were calculated for this expression, 26C plus 42, where C is the number of units taken per semester. So it says if Ian took 15 units in spring 2011, what was his tuition and fees? This 15, we have to decide what it means. So C is the number of units taken, and they just told us that Ian took 15 units. So C is going to be equal to 15. So when we rewrite this problem, we have 26 times 15, the number of units, plus 42. And again, I'm just going to go right over here to my calculator, 26, parentheses, one, five, close the parentheses, exactly like I see it. I don't really have to have those parentheses, but it doesn't hurt. And that's equal to 432. And what was his tuition and fees? That means it's in dollars, so this would be 432 dollars. All right, now we've got an interesting looking thing, expression P times the quantity one plus R to the T represents the amount of money in an account when P dollars is invested at an annual interest rate of R, and the notices as in decimal form, for T years. So find the amount of money that will be in the account at two years if 3200 dollars is invested at 4% annual interest rate. So we've got a P in our equation, and we've got an R in our equation, our expression, and we've got a T. So what do we know? 3200 is invested, so that's our P. P is the amount of money. And our rate is going to be 4%. So it says 4%, but it told us that it had to be in decimal form. So remember you move the decimal two places, one, two, and it becomes .04. And then the T is time, and that would be two years. So plugging in what we know then, 3200 times, and then we have 1 plus .04, that's a plus .04, to the T, two. And I, again, I'm just going to come right over here to my calculator and let it do all the work, 3200, parentheses, 1 plus .04, close the parentheses, and then remember exponents is carat, and then two, and press Enter. And we see that that's 3, 4, 6, 1.12. And what did we find? Find the amount of money. So it is an amount of money after two years. Two years. One final problem. The height of a baseball hit upward with an initial velocity of 95 feet per second from an initial height of 4.5 feet is represented by this. And there's your 95 and there's your 4.5. So they're already taken care of. Where T is the number of seconds after the ball has been hit. So what is the height of the ball after four seconds? Well, look at our variable, it's T. And we want to know after four seconds, so we're going to let that be 4. So negative 16 times 4 and then that squared plus 95 again times 4 and then plus 4.5. And again, just go right to your calculator. Most people would anyway, it's not really cheating if we had to pay for it. So carrot 2 plus 95 times 4, I'm just going to do multiplication and parentheses, plus 4.5 and enter. And we find out that it is 128.5. Okay, again, what did we find? What is the height? That's what they're asking us for. And height is in feet per second. The velocity was feet per second and the initial height was 4.5 feet. So we can easily say that it is 128.5 feet after four seconds, or at four seconds actually would be a better word. At four seconds, it's 128.5 feet in the air.