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I have three word problems here what I want to do in this video is not solve the word problems but just set up the equation that we could solve to get the answer to the word problems and essentially we're going to be setting up proportions in either case so in this first problem we have 9 markers cost $11.50 and then they ask us how much would 7 markers cost and let's just set X to be equal to our answer so X is equal to the cost of seven markers the cost of seven markers so the way to solve a problem like this is to set up two ratios and then set them equal to each other so you could say that the ratio of 9 markers to the cost of 9 markers so the ratio of the number of markers so 9 to the cost of the 9 markers to 1150 1150 this should be equal to the ratio of our new number of markers 7 equal to the new number of markers so that's 7 2 whatever the new cost or whatever the cost of 7 markers are 2x so let me do X in green 2 2 X so this is a completely valid proportion here the ratio of the of 9 markers to the cost of 9 markers is equal to 7 markers to the cost of 7 markers and then you could solve this to figure out how much those 7 markers would cost and you could flip both sides of this it would still be a completely valid ratio you could have 1150 11 52 9 so the ratio between the cost of 9 mark the ratio between the cost of the markers to the number of markers you're buying is equal to so 11:59 is equal to the cost of 7 markers is equal to 7 markers is the R is equal to the ratio of the cost of 7 markers to the number of markers which is obviously 7 so all I would did is flip both sides of this equation right here to get this one over here you could also think about you could also think about the ratios in other ways you could say that the ratio the ratio of 9 markers to 7 markers the ratio of 9 markers to 7 markers is going to be the same as the their cost is going to be the ratio is going to be equal to the ratio of the cost of 9 markers to the cost of 7 markers and then obviously you could flip both of these sides so you could say that the ratio of 7 markers then the same magenta color the ratio of 7 markers to 9 markers is the same thing as the ratio of the cost of 7 markers to the cost of 9 markers so that is 1150 so all of these would be valid proportions valid equations that describe what's going on here and then you could you would just have to essentially solve for x so let's do this one right over here 7 apples cost $5 how many apples can I buy with 8 dollars so once again we can say so we're going to assume that what they're asking is you know how many apples how many apples let's call that X X is what we want to solve for so 7 apples cost $5 so we have the ratio between the number of apples 7 and the cost of the apples 5 is going to be equal to is going to be equal to the ratio between another number of apples which is now X which is now X and the cost of that other number of apples and it's going to be 8 dollars and so notice here in this first situation what was unknown was the cost so we kind of had the number of apples to cost number of apples to cost now in this example the the unknown is the number of apples so number of apples to cost number of apples to cost and we could do all of the different scenarios like this you could also say the ratio between the ratio between 7 apples and X apples is going to be the same as the ratio between the cost of the cost of 7 apples and the cost of 8 apples and and obviously you could flip both sides of these either of these equations to get two more equations and any of these would be valid would be valid equations now let's do this last one so we have a cake recipe for five people I'll use new colors here a cake recipe for five people requires two eggs fires two eggs how many eggs so we want to know how many eggs so this will call X and you don't always have to call it X you could call it e for a while a isn't a good idea because he represents another number once you get to higher mathematics but you could call them you could call them Y or Z or any variable a B or C anything how many eggs do we need for a 15-person cake how many eggs do we need for a 15-person cake so you could say the ratio of people to eggs so the ratio of people to eggs is constant so if we have five people for two eggs for two eggs then for 15 people then for 15 people we are going to need X eggs this ratio is going to be constant 5 over 2 is equal to 15 over X or you could flip both sides of this or you could say the ratio between 5 and 15 the ratio between 5 and 15 is going to be equal to the ratio between the number of eggs for 5 people let me do that in that blue color the ratio between the number of eggs for 5 people and the ratio of the end and the number of eggs for 15 people and obviously you could flip both sides of this equation so all of these we've essentially set up the proportions that describe each of these each of these problems then you can go later and solve for X to actually get the answer