An artist invests in a mutual fund account paying 6 %, and ...

An artist invests in a mutual fund account paying $6 \%$, and $\$ 6000$ more than three times as much in a mutual fund account paying $5 \%$. Her total annual interest income from the investments is $\$ 825 .$ How much does she invest at each rate?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Percentage Calculation

This involves using the percentage rate to determine the interest earned on a principal amount. In particular, multiplying the investment amount by the interest rate (expressed as a decimal) yields the interest income, which is important in setting up the relations in the problem.

Translating Word Problems into Equations

This concept focuses on interpreting the language of a problem to form algebraic expressions and equations. It involves assigning variables to unknown quantities and using the relationships described in the problem to set up one or more equations.

System of Linear Equations

Creating and solving a system of linear equations is key to this problem. The situation provides two distinct relationships between the investment amounts and the interest income, leading to a set of simultaneous equations that must be solved to find the unknowns.

Algebraic Manipulation

Once the equations are set up, various algebraic techniques such as substitution or elimination are used to solve for the unknown variables. This includes isolating variables, combining like terms, and simplifying expressions to find a solution.

Transcript

Please give Ace some feedback