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# Modeling with one-step equations

CCSS.Math:

## Video transcript

Anna wants to celebrate her birthday by eating pizza with her friends for 40 to 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 40 to 50 total and I'll just write 42.5 especially because in all these choices they didn't write 40 to 50 they just wrote 42 point 5 which is which is equivalent so 40 to 50 that's the total amount the total the amount the total amount they spent on pizza and if I want to figure out how many pieces 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 and then 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 number of boxes now other ways that I could think about it I could say well what's the total that they spend so 40 to 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 a total they spend and this is 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 times forty two point five 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 and over here we it looks kind of like this except the p is on the wrong side this has 8.5 P is equal to 40 2.5 not forty two point five P is equal to eight point five and 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 point five is equal to 8.5 over P which is not true we have 8.5 times P is equal to 42 point 5 so this is this is not going to be the case and 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 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 right but now you would have forty two point five over eight point five 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 five hundred dollars 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 five hundred dollars and so they want to get a total of five hundred dollars and if each box is 275 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 this we've done this 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 275 to 275 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 the goal is to raise five hundred dollars so this they want this to be equal to five hundred dollars so this also could be an equation that the students could solve to figure out how many boxes of candy they need to sell