Question

ms. burke invested $27,000 in two accounts, one yielding 4% interest and the other yielding 11%. if she received a total of $1,640 in interest at the end of the year, how much did she invest in each account?
the amount invested at 4% was $\square.
the amount invested at 11% was $\square.

Explanation:

Step1: Define variables for investments

Let $x$ = amount invested at 4%, $27000 - x$ = amount invested at 11%

Step2: Set up interest equation

Total interest = 4% of $x$ + 11% of $(27000 - x)$
$$0.04x + 0.11(27000 - x) = 1640$$

Step3: Expand and simplify equation

$$0.04x + 2970 - 0.11x = 1640$$
$$-0.07x + 2970 = 1640$$

Step4: Isolate the $x$-term

$$-0.07x = 1640 - 2970$$
$$-0.07x = -1330$$

Step5: Solve for $x$

$$x = \frac{-1330}{-0.07} = 19000$$

Step6: Find 11% investment amount

$$27000 - x = 27000 - 19000 = 8000$$

Answer:

The amount invested at 4% was $\$19000$.
The amount invested at 11% was $\$8000$.