Question

mr p invested 250,000 into two different audiomobile companies. the first earned a 5 percent profit, and the seconed earned a 10 percent profit. if mr p made 3 times as much profit from the 10 percent investment as he did from the 5 percent investment, how much did he invest in the company that made 5 percent?

Answer 1

Let \( x \) be the amount Mr. P invested in the company that earned a 5% profit. Therefore, the amount he invested in the company that earned a 10% profit would be \( 250,000 - x \).

The profit from the first investment (5% profit) can be expressed as:
\[
\text{Profit from 5% investment} = 0.05x
\]

The profit from the second investment (10% profit) can be expressed as:
\[
\text{Profit from 10% investment} = 0.10(250,000 - x)
\]

According to the problem, the profit from the 10% investment is three times the profit from the 5% investment:
\[
0.10(250,000 - x) = 3 \times 0.05x
\]

Simplifying the equation:
\[
0.10(250,000 - x) = 0.15x
\]
\[
25,000 - 0.10x = 0.15x
\]

Now, combine like terms:
\[
25,000 = 0.10x + 0.15x
\]
\[
25,000 = 0.25x
\]

Now solve for \( x \):
\[
x = \frac{25,000}{0.25} = 100,000
\]

Thus, Mr. P invested \( \boxed{100,000} \) in the company that made a 5% profit.

To verify:
1. The amount invested in the 10% profit company is \( 250,000 - 100,000 = 150,000 \).
2. Profit from the 5% investment: \( 0.05 \times 100,000 = 5,000 \).
3. Profit from the 10% investment: \( 0.10 \times 150,000 = 15,000 \).
4. Check the relationship: \( 15,000 \) is indeed \( 3 \times 5,000 \).

The calculations are consistent, confirming that Mr. P invested \( \boxed{100,000} \) in the company that made a 5% profit.