Under selected conditions, a sedan gets 22 mpg in city...

Under selected conditions, a sedan gets 22 mpg in city driving and 32 mpg for highway driving. The model $G=\frac{1}{22} c+\frac{1}{32} h$ represents the amount of gasoline used (in gal) for $c$ miles driven in the city and $h$ miles driven on the highway. Determine the amount of gas required to drive $220 \mathrm{mi}$ in the city and $512 \mathrm{mi}$ on the highway.

Key Concepts

Substitution in Equations

Substitution is the process of replacing variables in an equation with specific values to calculate a precise outcome. This technique is fundamental in evaluating linear models and understanding how each component contributes to the final result, ensuring that abstract relations become concrete numerical answers.

Linear Models

A linear model is used to describe a situation where the relationship between variables can be represented by a linear equation. In applied mathematics, such models allow us to easily predict outcomes based on given inputs by assuming that the rate of change is constant, which is particularly useful when dealing with problems involving resource consumption or cost estimation.

Unit Rates

Unit rates describe how one quantity changes with respect to one unit of another quantity. In contexts like travel or fuel consumption, unit rates such as miles per gallon (mpg) are essential for converting trips or distances into the necessary resources required, thus enabling us to scale the relationship appropriately.

Arithmetic Simplification

Arithmetic simplification involves performing basic operations such as addition, multiplication, and division to reduce an expression to its simplest form. In the context of solving applied problems, this process ensures that the calculated results are both accurate and easily interpretable, which is critical in validating the model's predictions.

Transcript

Please give Ace some feedback