Ms. Burke invested ​$21 comma 000 in two​ accounts, one yielding 5​% interest and the other yielding 9​%. If she received a total of​ $1 comma 210 in interest at the end of the​ year, how much did she invest in each​ account?

Question

Question content area bottom
Part 1
The amount invested at 5​% was ​$
  
17,000.
Part 2
The amount invested at 9​% was ​$
  
enter your response here.

Answer 1

Let \( x \) be the amount invested at 5%, and \( y \) be the amount invested at 9%. According to the problem, we have the following two equations:

1. The total investment: \[ x + y = 21,000 \]

2. The total interest earned: \[ 0.05x + 0.09y = 1,210 \]

Now, we can solve this system of equations step by step.

Step 1: Solve for \( y \)

From the first equation, we can express \( y \) in terms of \( x \): \[ y = 21,000 - x \]

Step 2: Substitute into the interest equation

Substituting \( y \) into the second equation: \[ 0.05x + 0.09(21,000 - x) = 1,210 \]

Step 3: Distribute and simplify

\[ 0.05x + 1,890 - 0.09x = 1,210 \] \[ -0.04x + 1,890 = 1,210 \]

Step 4: Isolate \( x \)

Subtract \( 1,890 \) from both sides: \[ -0.04x = 1,210 - 1,890 \] \[ -0.04x = -680 \]

Step 5: Solve for \( x \)

Dividing both sides by -0.04: \[ x = \frac{-680}{-0.04} = 17,000 \]

Step 6: Find \( y \)

Now substitute \( x \) back into the equation for \( y \): \[ y = 21,000 - 17,000 = 4,000 \]

Final Answer

The amount invested at 5% was $17,000, and the amount invested at 9% was $4,000.