Toby split his savings into two different investments, one...

Toby split his savings into two different investments, one earning $5 \%$ and the other earning 7\%. He put twice as much in the investment earning the higher rate. In one year, he earned $\$ 665$ in interest. How much money did he invest in each account?

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Key Concepts

Simple Interest

Simple interest is a method of calculating the interest cost on a principal amount by multiplying the principal by the rate and the time period. It is used in situations where the interest does not compound, making the calculation straightforward and linear.

Ratio and Proportional Reasoning

Ratio and proportional reasoning involves comparing two quantities to determine how one quantity scales relative to another. This concept is critical when a problem specifies a relationship or multiple between different parts of an investment or any quantities.

Linear Equations

Linear equations are algebraic expressions that represent relationships where each term is either a constant or the product of a constant and a single variable. They are essential for modeling real-world scenarios, such as financial investments, where relationships between variables are directly proportional and can be manipulated to solve for unknowns.

Systems of Equations

Systems of equations consist of multiple linear equations that are solved together to find common solutions for the variables involved. This approach is especially useful in problems where there are multiple relationships or conditions that must all be satisfied simultaneously.

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