From the course: Preparing for the GMAT

Mixtures

From the course: Preparing for the GMAT

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Mixtures

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- [Instructor] So mixture word problems are somewhat common on the GMAT, so these are questions that ask about combining two or more things to form a composite. In this video, we'll go through an example of a mixture question, so let's look at this thing. While at work, Gabby accidentally mixed seven pounds of organic rainforest coffee beans with five pounds of conventional beans. So if the organic costs 15 bucks a pound, and the conventional ones costs $11 per pound, what should they price the mixture at per pound, if they want to be consistent? Huh, okay. So I like to think of these as basically averages. So remember the average equation? Let's just review that really quickly. The average equation is the sum of all the values that we're averaging, divided by the number of values that we're averaging. And that's going to equal our average. Great, right, so like, if I had three friends and their ages were 30, 40, and 50, I would find their average age by dividing by three and adding these all up. So let me just show you what that would turn into, it'd be 70 plus 50 is 120. Divided by three, which is 40. So just super quick review of averages. We're going to do the exact same thing here, with this mixture problem. Because we can think of it like an average. So if we start to set up that average equation. It's a fraction, and down here we want the number of things that we're averaging. Well, in this case, we are figuring out what should the mixture cost per pound, so we want the average price per pound. So we are averaging 12 pounds of coffee, right? 'Cause there's the seven plus the five. Great. And then the total cost is going to be our average. Now up here, on the numerator of the fraction, we have to represent 12 things. So the way that we can do that is we're going to say that there are seven pounds of the $15 per pound, and we're going to add that to the five pounds of the $11 per pound. So what this is doing is it's representing these 12 pounds of coffee. There's seven of the 15 bucks per pound, and then there five of the $11 per pound. And what this is giving us is a weighted average of the mixture. And when I say weighted, I mean it's kind of skewed towards the $15 per pound, because there's seven of those, seven pounds of the $15 per pound, and only five pounds of the $11 per pound. Okay, so let's do that math. Seven times 15 is 105. Plus five times 11 is 55. Divided by 12, and I'll simplify that to 105 plus 55, that's 160. Divided by 12, and let's see what that turns into. So it looks like it's going to be 13.3 repeating, so that looks a lot like answer choice C. So remember, if you're good at averages, you can be good at mixtures. In my opinion, the easiest way to solve a mixture question is to just set it up like an average equation, fill in everything you know, and then solve for the thing that you don't know.

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