Expert: Bobby Soltani - 3/10/2006

Question
Two stock investments cost $15,000. One stock then had a 40% gain and the other a 10% loss. If the net profit is $2000, how much was invested in each stock?

I need to know exactly how to break down this equation to solve. I have the solution, but I do not have a clue as to how they came up with the answers.

Thank you!

Answer
Hi Kim,

Let's let amount initially invested in the stock with the 40% gain be "a", and the one with the 10% loss be "b".

From the first sentence, we know that

a + b = 15000

A gain can be written as

(% gain)*initial investment.

So, a 40 percent gain can be written as

0.40*a

Likewise a 10% loss can be written as

0.10*b

From the second equation we know that

0.40*a - 0.1b = 2000

Now we have two equations and two unknowns and we can solve for a and b.

1) a + b = 15000

2) 0.40*a - 0.1b = 2000

Solve the first equation for a by subtracting b from both sides

a = 15000 - b

Plug 15000 - b in for a in the second equation.

0.40(15000 - b) - 0.1*b = 2000

Solve for b.

0.40(15000 - b) - 0.1*b = 2000

6000 - 0.4b - 0.1b = 2000

-.5b = -4000

b = 8000

plug 8000 in for b in the first equation to solve for a.

a + 8000 = 15000

a = 7000

So, 7000 was invested in the stock with the 40% gain, and 8000 was invested in the stock with the 10% loss.

Let me know if you have any questions.

Bobby