On a recent trip to the convenience store, you picked up 1...

On a recent trip to the convenience store, you picked up 1 gallon of milk, 7 bottles of water, and 4 snack-size bags of chips. Your total bill (before tax) was $17.00. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $2.00 more than a bottle of water, how much does each item cost?

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Key Concepts

System of Linear Equations

In many multi-step problems, several relationships between variables lead to a set of equations that you must solve together. This approach, known as forming a system of linear equations, enables you to harness the interconnections between the variables to find a unique solution for each, covering aspects like pricing and quantities.

Substitution Method

This algebraic strategy is crucial when solving systems of equations derived from word problems. By expressing one variable in terms of another and substituting this expression into another equation, the substitution method simplifies the system to a single-variable equation, facilitating the resolution of complex relationships and ultimately finding the values of all unknowns.

Word Problem Translation

This concept involves converting a written scenario into mathematical terms. In problems like this, you identify unknown quantities by assigning variables and then translate relationships and conditions stated in words into algebraic equations, setting a foundation for solving the problem.

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