need help with a story problem.?

Question

Susan invested part of her $18,000 bonus in a fund that paid 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 $780.

I need to find:
*amount invested at 9% = $________
*amount invested in stock = $_______



Thanks for your help!

Answer 1

Basic equation: Total Profit =SUM percent gain * amount invested
so let the fund investment be x
let the stock investment be 18000-x
From the basic equation:
0.09 * x -0.03 (18000-x) = 780
0.12 x = 1320
x = 11000, 18000-x = 7000

Answer 2

Let x = amount invested in a fund at 9%; $18,000 - x = amount invested in stock that suffered a 3% loss.

Equation:
(9% * x) - (3% * [$18,000 - x]) = $ 780
0.09x - ($540 - 0.03x) = $780
0.09x - $540 + 0.03x = $780
0.09x + 0.03x = $780 + $ 540
0.12x = $1,320
x = $1,320 / 0.12
x = $11,000

Answer:
Amount invested at 9% = $11,000
Amount invested at 3% = $7,000

Proof:
Profit: $11,000 at 9% = $990
Loss: $7,000 at 3%= $210
Net = $780

Answer 3

Answer is $11,000 invested in fund, $7,000 invested in stock.

x=amount invested in fund. y=amount invested in stock.
Equation 1. x+y=18,000. Equation 2. 9/100x-3/100y=780, so x+9/100x+y-3/100y=18780. Or 109/100x+97y=18780.
Have to subtract one equation from the other eliminating either x or y.
Multiply all parts of equation 1 by 109/100.
109/100x+109/100y=109/100 times 18,000 which is 19,620.
Subtract equation 2 from equation 1.
109/100x+109/100y=19,620
- 109/100x+97/100y= 18,780
= 0 +12/100y= 840,
12/100y=840 so y=840 times 100 divided by 12 which is 7,000. Y=7,000
Back to equation 1. x+y=18000. If y is 7000, x is 11,000.
Hope that helps.

Answer 4

Let
x be amount invested in fund
then (18000 -x) be the amount invested in stock

Profit on fund = 9% * x = 0.09x
Loss on stock = 3% * (18000 -x) = 540 - .03x

Net profit = profit (fund) - loss (stock)
780 = 0.09 x - (540 - 0.03x)
solve for x = 11,000 (invested in fund)
and 7,000 invested in stock

Answer 5

Let x = amount invested in a fund at 9% profit
y = amount invested in stock at 3% loss
$18,000 = total investment
$ 780 = net profit
_____________________________
Equations:
x + y = 18,000 (Eq. 1)
9%x - 3%y = 780 or
.09x - .03y = 780 (Eq. 2)
___________________________
x + y = 18,000 (Eq. 1)
x = 18,000 - y (Eq. 3)
Substitute Eq. 3 to Eq. 2 to find y
.09x - .03y = 780 (Eq. 2)
.09(18000- y) - .03y = 780
1620 - .09y - .03y = 780
1620 - .12y = 780
Transposition
1620 - 1620 - .12y = 780 - 1620
-.12y = -840
-.12y/-.12 = -840/-.12
y = $ 7,000 ==> amount invested in fund at 3% loss
Substitute the value of y in Eq. 1 to find x
x + y = 18,000 (Eq. 1)
x + 7,000 = 18,000
x = 18,000 - 7,000
x = $ 11,000 ==> amount invested in stock at 9% profit
==================
To check: x = 11,000, y = 7,000
.09(11,000) - .03(7,000) = 780
990 - 210 = 780
780 = 780

Answer 6

Let x = amount of money in the fund
18,000 - x = amount of money in stocks

0.09(x) - 0.03(18,000 - x) = 780
0.09x - 540 + 0.03x = 780
0.12x = 1,320
x = 11,000
and
18,000 - x = 7,000

Answer: amount invested at 9% = $11,000
amount invested in stock = $7,000