mrs psternak 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%?

Answer 1

Let \( x \) be the amount Mrs. Pasternak invested in the company that earned a 6% profit. Therefore, the amount invested in the company that earned a 12% profit would be \( 100,000 - x \).

The profit from the 6% investment is: \[ 0.06x \]

The profit from the 12% investment is: \[ 0.12(100,000 - x) = 12,000 - 0.12x \]

According to the problem, the profit from the 12% investment is twice the profit from the 6% investment. We can set up the equation: \[ 12,000 - 0.12x = 2(0.06x) \]

Simplifying the right side: \[ 12,000 - 0.12x = 0.12x \]

Now, combine the terms involving \( x \): \[ 12,000 = 0.12x + 0.12x \] \[ 12,000 = 0.24x \]

To find \( x \), divide both sides by 0.24: \[ x = \frac{12,000}{0.24} = 50,000 \]

Now we can find the amount invested in the 12% company: \[ 100,000 - x = 100,000 - 50,000 = 50,000 \]

Thus, the amount Mrs. Pasternak invested in the company that made 6% is: \[ \boxed{50,000} \]