Gas Station A gas station sells regular gas for 2.20 per...

Gas Station A gas station sells regular gas for $\$ 2.20$ per gallon and premium gas for $\$ 3.00$ a gallon. At the end of a business day 280 gallons of gas had been sold, and receipts totaled $\$ 680 .$ How many gallons of each type of gas had been sold?

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Key Concepts

Elimination Method

The elimination method involves adding or subtracting equations in a system to eliminate one of the variables, which simplifies the system into a single equation that can be solved more directly. This technique is particularly useful when the coefficients of one of the variables allow for their cancellation.

Substitution Method

The substitution method is a systematic approach for solving a system of linear equations by solving one of the equations for one variable and substituting that expression into the other equation. This reduces the system to one equation with one unknown, making it easier to solve.

Systems of Linear Equations

This concept involves representing problems with two or more unknowns by setting up a set of linear equations that capture the relationships described in the problem. Solving these systems allows one to determine the values of the unknowns simultaneously, which is essential in many real-world applications.

Translating Word Problems Into Equations

This key concept focuses on the ability to interpret verbal descriptions and convert them into algebraic equations. It is vital for understanding and representing real-world scenarios mathematically, enabling the use of algebraic methods to find solutions.

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