Mary has 3.00 in nickels, dimes, and quarters. If she has twice as many dimes as quarters and f

step 1 In the question it is given that the number of pennies is equals to number of nickels is equals

Mary has 3.00 in nickels, dimes, and quarters. If she has...

Key Concepts

Translating Word Problems to Equations

This concept involves reading and interpreting a problem statement to identify unknown quantities and the relationships between them. In many word problems, particularly those dealing with money or counts, the narrative information is converted into mathematical expressions or equations, which provides a structured way to start solving the problem.

Variable Assignment

Assigning variables is a foundational step in algebra where each unknown quantity is represented by a symbol. By doing so, given relationships or constraints, such as ratios or differences between quantities, can be clearly articulated and used to form equations.

System of Linear Equations

Once variables are assigned based on the word problem's information, multiple linear equations can be set up to reflect all given conditions. These systems are essential in capturing the various constraints simultaneously, such as fixed totals and proportional relationships between the unknowns.

Using the Substitution Method

The substitution method is a technique for solving systems of equations in which one variable is expressed in terms of another and then substituted into the remaining equations. This method simplifies the system, allowing for step-by-step solving of each variable sequentially, which is particularly effective when one equation provides a clear relationship between the variables.

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