Question

Susan Marciano invested part of her $32,000

bonus in a fund that paid a 9% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each investment if her overall net profit was $1,680.

The amount invested at 9%?

The amount invested in stock?

Answer 1

$22,000 was invested at 9%.

$10,000 was invested in stock.

Explanation:

Set up the equations:

x + y = $32,000 (equation 1)

0.09x - 0.03y = $1,680 (equation 2)

Solve equation 1 for x:

x = $32,000 - y

Substitute the expression for x in equation 2:

0.09($32,000 - y) - 0.03y = $1,680

Simplify equation 2:

$2,880 - 0.09y - 0.03y = $1,680

Combine like terms:

-0.12y = $1,680 - $2,880

Simplify further:

-0.12y = -$1,200

Divide by -0.12 to solve for y:

y = $10,000

Substitute the value of y back into equation 1 to solve for x:

x + $10,000 = $32,000

Simplify equation 1:

x = $22,000

The solution is:

$22,000 was invested at 9% profit.

$10,000 was invested in stock.