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Current time:0:00Total duration:4:12

Setting up a system of linear equations example (weight and price)

Video transcript

in this video we're going to get a little bit of practice setting up systems of linear equations based on a word problem we're not actually going to end up solving it you can do that if you like just for kicks but really we're going to just focus on setting it up so here we're told lauren uses a blend of dark roast beans and light roast beans to make coffee at her cafe she needs 80 kilograms of beans in total for her next order dark roast beans cost three dollars per kilogram light roast beans cost two dollars per kilogram and she wants to spend 220 dollars total let D be the number of kilograms of dark roast beans she buys and I'll be the number of kilograms of light roast beans she buys all right so based on this information that we've been given see if you can pause this video and set up a system of equations it's going to have two equations with two unknowns dnl that in theory we could solve to figure out the right number of kilograms of dark roast beans and light roast beans that Karen should use so pause this video and try to work that out all right now let's do it together and what I'm going to do is I'm gonna underline so let's see we know that D is dark roast beans and L is the number of kilograms of light roast beans and then they tell us here they say she needs 80 kilograms of beans in total so what we could say is hey the number of kilograms of dark roast beans plus the number of kilograms of light roast beans needs to be equal to 80 kilograms so the number of kilograms of dark roast beans plus the number of kilograms of light roast beans having trouble saying light roast beans well this what I just underlined here it says needs to be 80 kilograms in total so that needs to be 80 so this number of kilograms Plus this number kilograms is going to be equal to your total number of kilograms all right so I have one equation with two unknowns let's see if we can get another one so next they say dark roast beans cost three dollars per kilogram light roast beans cost $2 per kilogram and she wants to spend 220 dollars total so what I just underlined in this aquamarine color we can set up another equation with and if you haven't already set up your system of equations see if you can now do that see if you could set up the second equation pause the video all right well the way to think about is we just have to have an expression for how much does she spend on dark roast beans how much does she spend on light roast beans and then we need to add those two together and that needs to be equal to 220 dollars because that's how much she wants to spend in total so how much does she spend on dark roast beans well it's going to be the number of kilograms of dark roast beans that she buys and it says that it costs three dollars per kilogram so we're gonna multiply it by three three dollars per kilogram times the number of kilograms of dark roast beans this is how much she spends on dark roast beans and so how much is she going to spend on light roast beans well she buys L kilograms of light roast beans they told us that there and they cost two dollars per kilogram so two dollars per kilogram times the number of kilograms this is how much she spends on light roast beans so you add how much he spends on dark roast to how much he spends on light roast and so this is going to be two hundred and twenty dollars in total and there you have it we have our two equations with two unknowns and so now we could go and solve it but you can do that outside of this video but the whole point of this video is to understand how to construct these based on the constraints based on the information that we see in this so typically when you're trying to set these up there's often a sentence or two that will focus on one equation so this first one is saying hey the the kilograms let's add those up for the total number of kilograms and then there's another sentence or two that'll focus on in this case some other equation in this case it's the price so the price of the dark plus the price of the light is going to be equal to the total amount she wants to spend