Question

susan marciano invested part of her $21,000 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 $600
the amount invested at 10% is $\square
the amount invested in stock is $\square

Explanation:

Step1: Define variables for investments

Let $x$ = amount invested at 10% (profit).
Let $21000 - x$ = amount invested in stock (5% loss).

Step2: Set up profit equation

Profit from fund - Loss from stock = Net profit
$0.10x - 0.05(21000 - x) = 600$

Step3: Expand and simplify equation

$0.10x - 1050 + 0.05x = 600$
$0.15x - 1050 = 600$

Step4: Solve for $x$

$0.15x = 600 + 1050$
$0.15x = 1650$
$x = \frac{1650}{0.15} = 11000$

Step5: Find stock investment

$21000 - x = 21000 - 11000 = 10000$

Answer:

The amount invested at 10% is $\$11000$
The amount invested in stock is $\$10000$