Ivanna invested in her savings in two investment funds. The $8000 that she invested in Fund A returned a 2% profit. The amount that she invested in Fund B returned a 6% profit. How much did she invest in Fund B, if both funds together returned a 5% profit?

1 answer

Let the amount Ivanna invested in Fund B be \( x \). Then, the total amount invested in both funds is \( 8000 + x \).

The profit from Fund A, which she invested $8000 in at a 2% return, is:

\[ \text{Profit from Fund A} = 8000 \times 0.02 = 160 \]

The profit from Fund B, which she invested \( x \) in at a 6% return, is:

\[ \text{Profit from Fund B} = x \times 0.06 = 0.06x \]

To find the total profit from both funds, we sum the profits from Fund A and Fund B:

\[ \text{Total Profit} = 160 + 0.06x \]

We know that the total profit from both investments is also equivalent to a 5% return on the total investment. Thus, the equation for the total profit at a 5% return is:

\[ \text{Total Profit} = 0.05 \times (8000 + x) \]

Setting the two expressions for total profit equal, we have:

\[ 160 + 0.06x = 0.05(8000 + x) \]

Expanding the right side:

\[ 160 + 0.06x = 400 + 0.05x \]

Next, we will isolate \( x \). First, subtract \( 0.05x \) from both sides:

\[ 160 + 0.06x - 0.05x = 400 \]

This simplifies to:

\[ 160 + 0.01x = 400 \]

Next, subtract 160 from both sides:

\[ 0.01x = 400 - 160 \] \[ 0.01x = 240 \]

Now, divide by 0.01:

\[ x = \frac{240}{0.01} = 24000 \]

Thus, the amount Ivanna invested in Fund B is:

\[ \boxed{24000} \]