Final answer:
To determine the investment amounts, we can establish a system of equations based on the total investment, desired annual return, and the condition that the amount in the lowest interest account is double that of the highest interest account. By solving this system, we can find the specific allocations for the 3%, 4.5%, and 5% interest accounts to achieve a $1,900 annual return on a $50,000 total investment.
Step-by-step explanation:
The student's question is about how to allocate investments across three accounts to achieve a specific total annual return, with restrictions on the amount invested in each account based on the interest rates they offer. We can set up a system of equations to find the amount to invest in each account.
Given the information that Cyndee wants to invest $50,000 in total across the accounts, with the one at 3% interest being double what she invests in the one at 5% interest, and desires a total annual return of $1,900, the following equations represent the situation:
- x + y + z = 50,000 (total investment)
- 0.03x + 0.045y + 0.05z = 1,900 (total annual return)
- x = 2z (twice as much in the 3% account as in the 5% account)
To solve for x, y, and z, we can substitute x with 2z in both the total investment equation and the total annual return equation. Simplifying and solving this system of equations, we would find the amount to invest in each account to meet Cyndee's requirements.