Using Models Use the model given to answer the questions...

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?

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?

Key Concepts

Mathematical Modeling

Mathematical modeling involves creating mathematical representations of real-world situations to analyze and make predictions. In this context, the model is an equation that relates the dependent variable to independent variables by expressing the relationships between different quantities, allowing one to compute an unknown value when given others.

Ratios and Proportions

This concept deals with the comparison of two quantities by division, resulting in a unit rate that expresses the relationship between them. The model used here, which involves a ratio of miles driven to gallons of gas, is an example of using proportions to measure and compare efficiency in practical scenarios.

Solving Equations

Solving equations is a fundamental process in algebra where one determines the value of unknown variables. In such models, rearranging the equation to isolate the desired variable allows one to compute specific quantities, whether it’s finding a rate or determining the amount of a resource used.

Transcript

00:01 Hey guys and welcome to numerary, a fantastic tool and resource to help you master any topic in the stem field.

00:08 My name is alex and today i will be helping you do a real -life scenario algebra problem.

00:14 All right, let's get started.

00:16 So as you can see, here's our problem.

00:18 The gas mileage m in millgal of a car is modeled by m equals n divided by g, where n is the number of miles driven and g is the number of gallons of gas used.

00:29 And as you can see, we have two parts to this problem, part a and part b.

00:34 Let's start with part a.

00:37 Okay, part a.

00:39 The best way to start when given a word problem is to highlight or underline the most important variables and information.

00:46 So a, find the gas mileage m for a car that drove 240 miles on eight gallons of gas.

00:53 So already we have three variables that stand out to us.

00:57 We have m.

00:59 I'm going to write it here.

01:00 We have m.

01:03 We have n and we have g.

01:10 And we can see this from up top right here.

01:14 The gas model m in milgal of a car is modeled by m equals n divided by g.

01:19 Where n, see it already tells us what n is, n is the number of miles driven, and g is the number of gallons of gas used.

01:28 So from this information, we can tell that m equals the gas mileage, which i will abbreviate gm, n equals the number of miles driven.

01:45 So i'm just going to write miles driven.

01:59 And g, you can guess.

02:01 That is the number of gallons of gas use.

02:04 So i'm just going to write g of you.

02:10 You.

02:11 So that way you can tell that it's gallons of gas used.

02:16 Now that we've labeled these, we can also note that we can take out of this problem an equation.

02:24 And the equation was actually given to us.

02:27 You know what the equation is? the equation is right here when this is modeled by m equals n divided by g.

02:35 So let's write that down.

02:36 We'll write it right here.

02:38 So m equals n divided by g.

02:46 I'm sorry this looks like a w.

02:47 Let me fix that.

02:50 All right.

02:52 Now that we have all the key parts of the problem highlighted and underlined, let's break it down.

02:57 So ask yourself, what are we trying to find? what are we trying to find? what we are trying to find out is gas mileage, which we know is represented by the variable m.

03:08 So if you forget, we have it right here.

03:13 I'll do it in blue.

03:14 We have gas mileage.

03:17 And this is, and in the problem, in part a, we can see find the gas mileage m.

03:23 Okay.

03:24 From the problem, we already know are n and g variables.

03:27 N in red, n equals 240.

03:35 And in blue, g is 8.

03:39 So let's substitute our variables for numbers...