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Using Models Use the model given to answer the questions about the object or process being modeled.
The gas mileage $M($ in milgal) of a car is modeled by $M=N / G,$ where $N$ is the number of miles driven and $G$ is the number of gallons of gas used.(a) Find the gas mileage $M$ for a car that drove 240 mi on 8 gal of gas.(b) $A$ car with a gas mileage $M=25$ mi/gal is driven 175 mi. How many gallons of gas are used?
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Hey, guys. And welcome to New Marie. A fantastic tool and resource to help you master any topic in the stem field. My name is Alex, and today I will be helping you through a real life scenario. Algebra problem. All right, let's get started. So as you can see, who is our problem? The gas mileage am in mill girl off a car is modeled by M equals and divided by G, where n is the number of miles driven and G is the number of gallons of gas used. And as you can see, we have two parts to this problem are a in part B. Let's start with car, eh? Okay, our day bet way this But when given a work problem is the highlight or underlined the most important valuables and information. So it find the gas mileage M for a car that drove drawing for 40 miles on eight gallons of gas. So already we have three variables that stand out. Plus, we have m when you're ready. Here we have m. We have end and we have G and we can see this from off pop. Right here. The gas mileage in Mill Girl of a car is modeled by Emmett Equals n divided by G Where end See, it already tells us what Venice and is the number of miles driven and G is the number of gallons of gas used. So from this information with Intel that M equals the gas mileage travel. Abbreviate GM end equals the number of miles driven. So I'm just gonna write miles dripping and G You can guess that is the number of gallons of gas use. Something's going right, Jeanne Um, you two. That way you can tell that it's gowns of gas used. Yeah, now that we've labeled these, we can also know that we can take out of this problem and equation. And the question was actually given to us. You know what? The quickness. The equation is right here when this is modeled by m m equals n divided by G. So let's write that down. We'll write it right here. So am I equals and divided by G. I'm sorry. This looks like a W. Let me fix that. All right now that we have all the key parts of the problem, Highlight didn't underlined. Let's break it down. So ask yourself. What are we trying to find? What are we trying to find out? What we're going to find out is gas mileage, which we know is represented by the variable M. So if you forget, we have it right here, do it in blue. We have gas mileage, and this is in the problem. But in part A, we could define the gas mileage M okay, but we already know our end n G variables. And in red equals 240 And in blue G is eat. No, it's up to you are variables for numbers formula should now look like this. It's now we should have and equals 240 which is our a divided by G, which is eight now. It's a simple division problem. What is 240 divided by eight. Solve that and you have your answer for gas mileage. Super simple, right? All right, let's put apart. Be now. I'll be So what do we need to find out? Ask yourself. I need to find out how many gallons of gas was used. If you thought that, then you'd be correct. And you already have the variables labeled from the last problem. So m we know and we know is gas mileage and and we know is number miles, German cell say number miles driven. And G you know what she is? Ji is the number of gallons used by the car. So I'm just gonna say gow used All right, now that we reiterated our variables No, nothing. So, no, what is our home and what is our equation? So we know that the m our gas mileage equals 25 and we know this because of up here, it's in our problem. And what is our miles German? We know that our miles driven is 175. So we need to find G. No, The formula that we need to solve to solve this problem is what we used is similar to what we used in part a This equation right here we're gonna take this and use it in part B. So let me rewrite that equation and equals and divided by G. So we know that this we know that in this problem we need to solve for G. So what, we're gonna do this swamp that m energy? Very bills. So we have a new equation for equation will now look like this. You know, doing any red Our question will now equals g equals and provided by M. This is our new equation. And we use this. We changed the equation because now we're finding gallons of gas used to that rg. And now we have to do a substitute. Our letters. Four numbers. So then our equation will look like G equals 1 75 provided by 25. And we know this because M equals 25 which we have here and end equals 175. Now it's a simple division problem. Last time. So all you have to do is 175 divided by 25 then you have your G I hold is helped things.
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