Lottery Winnings Linda won 200,000 in a state lottery. She...

Lottery Winnings Linda won $\$ 200,000$ in a state lottery. She first paid income tax of $30 \%$ on the winnings. She invested some of the rest at $1.5 \%$ and some at $4 \$ 6$, earning $\$ 4350$ interest per year. How much did she invest at each rate?

Key Concepts

Percentage Calculation

This concept involves calculating parts of a whole based on a given percentage. It is used to determine amounts such as taxes or discounts by multiplying the total by the percentage expressed as a decimal, which is fundamental in financial calculations and budgeting.

Interest Rates

Interest rates represent the proportion of a sum of money charged or earned per unit time, generally expressed as a percentage. Understanding interest rates is essential for comparing different investment or loan options and for calculating the potential returns or costs associated with financial transactions.

System of Linear Equations

A system of linear equations is a collection of two or more linear equations involving the same set of variables. Solving such systems allows one to find the unique values of those variables that satisfy all the equations simultaneously, which is crucial in problems where relationships between multiple quantities must be determined.

Mixture Problems

Mixture problems involve combining two or more components with different properties in order to achieve a desired total quantity or characteristic. In financial contexts, this often entails determining the amounts of funds to invest at different rates to meet a specific overall return, requiring the formulation and solution of equations based on the given conditions.

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