Linear inequality word problems — Basic example

- [Professor] A convenience store requires that Ayumi spend $4 or more if she wants to pay using a debit card. Donuts each cost $.80, donuts each cost $.80 or $.80 each. A bottle of orange juice costs $1.20. If d represents the number of donuts Ayumi would need to buy to pay for one orange juice and the donuts using a debit card, which of the following inequalities best models the situation described above? Alright, 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 donuts, d represents the number of donuts. So let's write this down, so this one orange juice, this one orange juice right over there, that's going to be $1.20, we'll assume everything I'm writing is in dollars, that's that and then how much is she gonna spend on donuts? Well, the donuts are $.80 each and d is the number of donuts, so she's gonna spend $.80 times d or 0.80d we could write it like that, or we could just write this as 0.8, 0.8d so this is what she's spending on that one orange juice, this is what she's spending on that d donuts and in order to use her debit card, in order to use her debit card, she needs to spend $4 or more, so that this thing right over here needs to be greater than or equal to $4, once again, greater than $4, that's the or more, but it could also be exactly $4 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, you have .8d plus 1.2 is greater than four so before you even see if this expression right over here is equivalent to this expression right over here, you could see this is greater than four, we wanna be greater than or equal to four, so just like that you could rule this one out and actually if you distribute the 0.8d you will see that you get something different, you get 0.8d and then 0.8 times 1.2 is not $1.20 it's not 1.2 right over here, so we can rule that one out. 0.8d times d plus 1.2 is greater than or equal to four, well let's see, that has a greater than or equal to but if you distribute 0.8d, 0.8 times d is going to be this but 0.8 times 1.2 is not 1.2 it's going to be .96 so 0.96, so that's not going to work out. Let's see, 0.8d plus 1.2 is greater than four, we're close, but remember we want greater than or equal to four, 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 $1.20, they wrote 1.2, so if you just swap these two around you get, let me do that in those same colors, you get 0.8d plus, instead of writing $1.20 I'll just write 1.2 is greater than or equal to four, is greater than or equal to four, so this is exactly what we had over there so I would definitely feel good about picking this one. Now if you're doing this in really kind of timed conditions, I would, instead of even doing this, you could go straight, instead of just even trying to think it through you good go straight to say well, which of these really describes what's going on here? So let's see, we wanna be greater than or equal to 4$, we're gonna spend $1.20 on orange juice and then the amount that we spend 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.