Lottery Winnings. After winning 60,000 in the lottery, a...

Lottery Winnings. After winning $\$ 60,000$ in the lottery, a retired teacher gave $\$ 10,000$ of it to her grandchildren. She invested part of the remainder in a growth fund that earned $4.4 \%$ annully and the rest in certificates of deposit paying a $5.8 \%$ annual percentage yield. The interest that she received on these two investments totaled $\$ 2,732$ at the end of the first year. Find the amount of each investment.

Lottery Winnings. After winning $\$ 60,000$ in the lottery, a retired teacher gave $\$ 10,000$ of it to her grandchildren. She invested part of the remainder in a growth fund that earned
$4.4 \%$ annully and the rest in certificates of deposit paying a $5.8 \%$ annual percentage yield. The interest that she received on these two investments totaled $\$ 2,732$ at the end of the first year. Find the amount of each investment.

Key Concepts

Algebraic Modeling

This concept involves translating word problems into mathematical equations by defining variables for unknown quantities and creating expressions that represent relationships described in the problem. It is fundamental in problems where real-life situations, like investment allocations and interest earnings, need to be expressed in algebraic form.

System of Linear Equations

In problems with multiple unknowns, setting up a system of linear equations allows for the simultaneous resolution of these variables. The equations are derived from the total amounts invested and the total interest earned, and solving them provides the specific values for each investment component.

Interest Rate Calculation

This concept involves applying percentage rates to determine the earnings on a principal investment over a certain period. Understanding how to compute interest by multiplying the principal amount by the annual percentage yield is key in evaluating and comparing different investment returns.

Investment Allocation

Investment allocation refers to the process of deciding how to distribute a given sum of money across different investment vehicles. It involves determining the amount invested in each option based on conditions like varying interest rates and desired total outcomes, which is a common problem in financial planning and portfolio management.

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