Question

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:
\[
\boxed{50,000}
\]