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Linear inequality word problems — Basic example

Video transcript

a convenience store requires that a Yumi spend $4 or more if she wants to pay using a debit card doughnuts each cost 80 cents doughnuts each cost 80 cents or 80 cents each a bottle of orange juice costs a dollar 20 if d represents the number of doughnuts a ume would need to buy to pay for one orange juice and the doughnuts using a debit card which of the following inequalities best models the situation described above all right so she needs to spend $4 or more and she's going to buy one orange juice she's going to buy one orange juice and D doughnuts D represents the number of doughnuts so let's let's write this down so this one orange juice this one orange juice right over there that's going to be a dollar 20 we'll assume everything I'm writing is in dollars that's that and then how much is she gonna spend on doughnuts well the doughnuts are 80 cents each and D is the number of doughnuts so she's gonna spend 80 cents times d or 0.8 zero D we could write it like that or we could just write this as 0.8 0.8 D so this is what she's spending on that one orange juice this is what she's spending on the D doughnuts and in order to use her debit card in order to use her debit card she needs to spend 4 dollars or more so this thing right over here needs to be greater than or equal to 4 dollars once again greater than 4 dollars that's the or more but it could also be exactly 4 dollars and that's why we have the equal sign right over here so let's see which of these choices describe that let's see if point 8 D plus 1 point 2 is greater than 4 so before you even see if this expression right over here is equivalent to this expression right over here you can see this is greater than 4 we want to be greater than or equal to 4 but so just like that you could you could rule you could rule this one out and actually if you multi you will see that you get something different you'd get zero point eight d and then zero point eight times one point two is not one point is not a dollar 20 is not 1.2 right over here so we can rule that one out 0.8 d+ 1 point 0.8 times D plus 1 point 2 is greater than or equal to 4 well let's see that that has the greater than or equal to but if you distribute 0.8 D 0.8 times D is going to be this but 0.8 times 1.2 is not 1.2 it's going to be it's going to be 0.96 0.96 so that's that's not going to work out let's see 0.8 D plus 1 point 2 is greater than 4 we're close but remember we wanted greater than or equal to 4 and then lucky for us this right over here is very similar it's exactly what we wrote up here with just the difference that instead of writing a dollar 20 they wrote 1.2 so if you just swap if you just swap these two around you get you get 0 let me do them in those same colors you get 0.8 D plus instead of writing a dollar 20 I'll just write 1.2 is greater than or equal to 4 is greater than is greater than or equal to 4 so this is exactly what we had over there so I would definitely feel good about picking this one now if you're doing this in really kind of time conditions I would instead of even doing this you could go straight you could instead of just even trying to think it through you could go straight to C well which of these really describes what's going on here let's see we want to be greater than or equal to $4 we're gonna spend a dollar 20 on orange juice and then the amount that we spent on donuts is that right over there so you might have been able to just cut to the chase and pick that one whichever way works better for you