Translate to a system of equations and solve. Sam invested ...

Translate to a system of equations and solve.
Sam invested $\$ 48,000,$ some at $6 \%$ interest and the rest at $10 \%$. How much did he invest at each rate if he received $\$ 4000$ in interest in one year?

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Key Concepts

System of Equations

A system of equations involves two or more equations with a set of shared variables. This concept is essential for solving problems where multiple relationships must be satisfied simultaneously, allowing us to determine the values of unknown quantities.

Translating Word Problems

This is the process of converting a real-life scenario into mathematical expressions or equations. It involves identifying key information, defining variables, and using the given relationships to form equations that accurately represent the problem.

Investment Interest Calculations

Understanding investment interest calculations involves applying the formula Interest = Principal × Rate. This concept is central to problems involving financial investments where different portions of capital are subject to varying interest rates.

Solving Linear Equations

This involves techniques such as substitution and elimination to find the values of unknown variables in one or more linear equations. Mastery of these methods is fundamental in determining solutions that satisfy all conditions set by a system of equations.

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