Solve each problem by using a system of three equations in...

Solve each problem by using a system of three equations in three unknowns. Salvador's Fruit Mart sells variety packs. The small pack contains three bananas, two apples, and one orange for 1.80 dollars . The medium pack contains four bananas, three apples, and three oranges for 3.05 dollars. The family size contains six bananas, five apples, and four oranges for 4.65 dollars . What price should Salvador charge for his lunch-box special that consists of one banana, one apple, and one orange?

Solve each problem by using a system of three equations in
three unknowns.

Salvador's Fruit Mart sells variety packs. The small pack contains three bananas, two apples, and one orange for 1.80 dollars . The medium pack contains four bananas, three apples, and three oranges for 3.05 dollars. The family size contains six bananas, five apples, and four oranges for 4.65 dollars . What price should Salvador charge for his lunch-box special that consists of one banana, one apple, and one orange?

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Key Concepts

Elimination Method

The elimination method is a strategy for solving systems of linear equations by combining the equations to cancel out one or more variables. This reduction simplifies the system, often transforming it into one that involves fewer variables, and is a foundational technique in solving multi-variable problems.

System of Linear Equations

A system of linear equations consists of multiple equations that involve the same set of variables. The aim is to find the values of these variables that satisfy all the equations simultaneously. This concept is central to many areas in mathematics as it provides a structured method for dealing with multiple constraints at once.

Variable Representation

Variable representation involves assigning symbols to unknown quantities, which then allows the creation of equations that model real-world situations. This abstraction is key for translating a problem stated in words into a mathematical framework where algebraic techniques can be applied.

Translating Word Problems into Equations

This concept involves interpreting a narrative or descriptive problem and identifying the relationships between quantities. The key step is to extract the relevant information from the context and express it as algebraic equations, usually setting the stage for solving using systematic methods.

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