Kelly saves all of her dimes and nickels in a jar on her...

Kelly saves all of her dimes and nickels in a jar on her desk. When she counts her money, she finds that she has 133 coins worth a total of $\$ 10.45 .$ How many dimes and how many nickels does she have?

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Key Concepts

System of Linear Equations

This concept involves setting up multiple equations that describe relationships between unknown quantities. In many coin problems, one equation represents the total number of coins and another reflects the total monetary value. Solving this system allows us to find the individual counts of each type of coin.

Variable Assignment

In creating equations, unknown values are often represented with variables. Assigning variables to the different categories (such as different coins) helps to organize the information from the word problem and formulate precise equations for further mathematical processing.

Equation Formulation

This key concept involves translating worded conditions into mathematical equations. For coin problems, one must establish equations based on the total count of coins and the corresponding total monetary value, ensuring that each coin's specific monetary value is accurately accounted for.

Methods for Solving Systems

Techniques such as substitution or elimination are used to solve systems of equations. By expressing one variable in terms of another or combining equations, these methods provide the means to isolate each variable and determine the unique solution that satisfies the problem's constraints.

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