(d) When the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee (4 cups = 1 qt). How many kg of coffee are required to produce 200 cups of coffee?

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Hello. Everyone in this video. We're going to be doing some dimensional analysis and how I want to start off my dimensional analysis problem is by starting out my information what we're given and what we're trying to find. So let's start off by writing out what we are given. So what I see that I'm given is that for every 50 g of tea leaves that contains 200 mg of caffeine, were also given The 85 g of caffeine that they want to kind of investigate. And our goal here or where we're trying to find is going to be the mass of tea leaves. Alright, so this is kilo grams. Alright, so starting off my dimensional analysis, I'm going to be starting off with the end goal which is this one right here. So the 85 g of caffeine. So I can see here that we have some sort of mass unit of caffeine as well for another piece of the information. However, I can go ahead and directly plug this into here because we have grams and milligrams, it won't really do much. And if we went ahead to plug it in. So I want to first convert this crams into milligrams and then we can plug in this given information. The first step is to convert grams into milligrams. So I know for every one g of caffeine There's going to be 1000 milligrams of caffeine. Maybe I can extend this a little bit. Alright, perfect. So we can see here that the grams of caffeine will cancel out nicely And then from Milligrams we go two g next. So multiplying that unit, we know that we have this conversion right over here that we can now plug in. So On the denominator, I want to go ahead and cancel out that caffeine. So I'll put 200 mg of that caffeine, Maybe extending this fraction bar a little bit. And then on top will be our 50 g of T leaves. Okay? And as you can see, the milligrams of caffeine will cancel out. Now we're left with the grams of tea leaves essentially. We want to go ahead now and finally find the kilograms. So we know the direct conversion from grams to kilograms. Let's go ahead and insert that fraction bar. Alright, so I know for everyone, kilo ground Is going to equal to g and to cancel out the units grams with grams. Leaving us with the desired kilograms of tea leaves. And that's exactly what we're looking for. As for the numerical value, plugging in all this into my calculator, It will result in a value of 21.25 kilograms of tea leaves. And that's going to be my final answer for this problem

(d) When the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee (4 cups = 1 qt). How many kg of coffee are required to produce 200 cups of coffee?

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Key Concepts

Conversion between units

Proportional relationships

Dimensional analysis