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 1 year, he earned $\$ 665$ in interest. How much money did he invest in each account?

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Key Concepts

Word Problem Translation

Word problem translation is the process of converting real-world scenarios into mathematical models. It involves defining variables, identifying relationships, and setting up equations based on verbal descriptions, which is a critical skill for solving algebraic problems in various practical contexts.

Ratios and Proportions

Ratios and proportions allow comparative reasoning between quantities by expressing one quantity as a multiple or fraction of another. This concept is especially useful when distributing or comparing parts of a whole, and it simplifies the formation of equations by reducing the number of independent variables.

Simple Interest

Simple interest is a method for calculating the interest on an investment or loan where the interest is determined solely based on the original principal amount, without compounding. This concept is fundamental in finance and algebra, as it relates the rate of return to the principal and time period in a linear fashion.

Systems of Linear Equations

Systems of linear equations involve multiple equations that share common variables. This technique is used to analyze relationships between various quantities in a problem, allowing one to solve for unknowns by finding a set of values that satisfies all the equations simultaneously.

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