Modeling with one-step equations

- [Voiceover] Anna wants to celebrate her birthday by eating pizza with her friends. For $42.50 total, they can buy p boxes of pizza. Each box of pizza costs $8.50. Select the equation that matches this situation. So before I even look at these, let's see if I can make sense of the sentence here. So for $42.50 total, and I'll just write 42.5, especially because in all these choices they didn't write 42.50, they just wrote 42.5 which is equivalent. So 42.50 that's the total amount they spent on pizza and if I wanted to figure out how many boxes of pizza they could buy, I could divide the total amount they spend, I could divide that by the price per box. That would give me the number of boxes. So this is the total, total dollars. This right over here is the dollar per box and then this would give me the number of boxes. # of boxes. Now other ways that I could think about it. I could say, well what's the total that they spend? So 42.50, but what's another way of thinking about the total they spend? Well you could have the amount they spend per box, times the number of boxes. So this is the total they spend and this another way of thinking about the total they spend, so these two things must be equal. So let's see, if I can see anything here that looks like this, well actually this first choice, this, is exactly, is exactly what I wrote over here. Let's see this choice right over here. P is equal to 8.5 x 42.5. Well we've already been able to write an equation that has explicitly, that has just a p on one side and so when you solve for just a p on one side, you get this thing over here, not this thing, so we could rule that out. Over here it looks kind of like this, except the p is on the wrong side. This has 8.5p is equal to 42.5, not 42.5p is equal to 8.5. If we try to get the p on the other side here, you could divide both sides by p, but then you would get p divided by p is one. You would get 42.5 is equal to 8.5/p which is not true. We have 8.5 times p is equal to 42.5, so this is, this is not going to be the case. One thing to realize, no matter what you come up with, if you came up with this first, or if you came up with this first, you can go between these two with some algebraic manipulations. So for example, to go from this blue one to what I wrote in red up here, you just divide both sides by 8.5. So you divide by 8.5 on the left, you divide 8.5 on the right. Obviously to keep the equal sign you have to do the same thing to the left and right, but now you would have 42.5/8.5 is equal to, is equal to p. Which is exactly what we have over there. Let's do one more of these. Good practice. Mr. Herman's class is selling candy for a school fundraiser. The class has a goal of raising $500 by selling c boxes of candy. For every box they sell, they make $2.75. Write an equation that the students could solve to figure out how many boxes of candy they need to sell. How many boxes of candy they need to sell. Well there's a couple of ways you could think about it. They have a goal of raising $500 and so they want to get a total of $500, and if each box is $2.75, divide the total by the amount they get each per box and then this is going to be equal to the number of boxes that they need to sell. So this we've done. This is an equation that the students could solve to figure out how many boxes of candy they need to sell. Another way you could think about it, it's 2.75 per box times c boxes. This is the total amount of money they will raise. Whoops, this is the amount. So this is the amount that they will raise and their goal is that, their goal is to raise $500. So they want this to be equal to $500. So this also could be an equation that the students could solve to figure out how many boxes of candy they need to sell.