Question

susan marciano invested part of her $37,000 bonus in a fund that paid a 10% profit and invested the rest in stock that suffered a 5% loss. find the amount of each investment if her overall net profit was $1,950. the amount invested at 10% is $\square. the amount invested in stock is $\square.

Explanation:

Step1: Define Variables

Let \( x \) be the amount invested at 10% (in the fund), and \( y \) be the amount invested in stock. We know that the total bonus is $37,000, so LXI2. The profit from the fund is LXI3, and the loss from the stock is LXI4. The overall net profit is $1,450, so the equation for profit is \( 0.10x - 0.05y = 1450 \).

Step2: Solve the System of Equations

From the first equation, we can express \( y \) as \( y = 37000 - x \). Substitute this into the second equation:

$$ 0.10x - 0.05(37000 - x) = 1450 $$

Expand the equation:

$$ 0.10x - 1850 + 0.05x = 1450 $$

Combine like terms:

$$ 0.15x - 1850 = 1450 $$

Add 1850 to both sides:

$$ 0.15x = 1450 + 1850 $$

$$ 0.15x = 3300 $$

Divide both sides by 0.15:

$$ x = \frac{3300}{0.15} = 22000 $$

Step3: Find the Amount Invested in Stock

Now that we know \( x = 22000 \), substitute back into \( y = 37000 - x \):

$$ y = 37000 - 22000 = 15000 $$

Answer:

The amount invested at 10% is $22,000.
The amount invested in stock is $15,000.