Question

You decided to invest $10,000 that you won in a contest. You found three accounts to divide your money into. One account pays 5% interest, the other pays 7% interest and the last account pays 10%. You can only put half the amount in the 10% account than you put in the 5% account. At the end of the year you earned $670 in interest. How much did you invest in each account? Write your answer as an ordered triple in the correct order (amount in 5%, 7% and 10%)​

Answer 1

In a system of equations problem, the student is looking to split $10,000 into three investment accounts with different interest rates to earn a total of $670 by the end of the year. By defining variables for each account and setting up equations based on the total investment and the condition that the 10% account has half the amount of the 5% account, we can solve the system to find the investment distribution.

Step-by-step explanation:

The student has won $10,000 and is interested in dividing this sum into three separate accounts offering different interest rates, with some additional conditions. We are tasked with calculating how much to invest in each account to earn a total interest of $670 at the end of the year. This is a problem involving a system of equations.

Let's denote the amount invested in the 5% account as x, the 7% account as y, and the 10% account as z. According to the conditions, we have the following equations:

• x + y + z = $10,000 (the total amount of money to be invested)
• 0.05x + 0.07y + 0.10z = $670 (the total interest earned at the end of the year)
• z = 0.5x (half of the amount in the 10% account is put in the 5% account)

Through substitution and solving the system of equations, we can find the values of x, y, and z. The final answer will be presented as an ordered triple, representing the amounts invested in the accounts with 5%, 7%, and 10% interest rates, respectively.