SOLUTION: Here's my question: Mrs. Pasternak invested $100,000 in two different healthcare companies. The first earned a 6% profit, and the second earned a 12% profit. If Mrs. Pasternak m

Question 1039073: Here's my question:
Mrs. Pasternak invested $100,000 in two different healthcare companies. The first earned a 6% profit, and the second earned a 12% profit. If Mrs. Pasternak made 2 times as much profit from the 12% investment as she did from the 6% investment, how much did she invest in the company that made 6%?
I think it's set up like Is this right? If not, how should I do it?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i would say she invested 50,000 in each.
the reason is that 12% is two times 6%, so if she made twice as much profit from the 12% investment as she made from the 6% investment, she had to invest the same amount in each.

50,000 * .06 = 3000
50,000 * .12 = 6000

you can also solve this algebraically as follows:

x = the 6% investment
y = the 12% investment
p = profit
x + y = 100,000
.06x + .12y = p

you are given that the profit from the 12% investment is twice the profit from the 6% investment.

the equation for that is .12 * y = 2 * .06 * x

simplify this equation to get .12 * y = .12 * x
solve for y to get y = .12 * x / .12
simplify to get y = x.

in the equation of x + y = 100,000, replace y with x to get x + x = 100,000.
simplify to get 2*x = 100,000
divide both sides of the equation by 2 to get x = 50,000

since x = 50,000, then y must also be equal to 50,000.

the profit equation of .06 * x + .12 * y = p becomes .06 * 50,000 + .12 * 50,000 = p

simplify to get 3000 + 6000 = p

p is equal to 9000.

the profit on the 12% investment is twice the profit on the 6% investment.

my intuition up front was ok and the algebra supported it.

Answer by MathTherapy(10557) (Show Source): You can put this solution on YOUR website!
Mrs. Pasternak invested $100,000 in two different healthcare companies. The first earned a 6% profit, and the second earned a 12% profit. If Mrs. Pasternak made 2 times as much profit from the 12% investment as she did from the 6% investment, how much did she invest in the company that made 6%?
I think it's set up like Is this right? If not, how should I do it?

No, you can't set it up like that!
Do it as follows:
Let the amount invested in the 6% fund, be S
Since a total of $100,000 was invested, then amount invested in the 12% fund = 100,000 - S
Profit from 6% fund: .06S, and profit made from the 12% fund = .12(100,000 - S)
Now, since the 12% fund earned twice the profit made from the 6% fund, then we can say that: .12(100,000 - S) = 2(.06S)
12,000 - .12S = .12S
12,000 = .12S + .12S
12,000 = .24S
S, or amount invested in the 6% fund =
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