Answer:
The answer is that the actor invested $ 107,000 at 7% and $ 470,000 at 11%.
Step-by-step explanation:
1. Let's check the information provided to us to answer the problem correctly:
Two different interest rates from the investments:
7% from some money
11% from US$ 42,000 + four times the amount invested at 7%
Total annual interest earnings from both investments = US$ 59,190
2. How much did the actor invest at each amount? Use the six-step method.
x = Money invested at 7%
4x + 42,000 = Money invested at 11%
7% = 0.07, 11% = 0.11
3. Now, we can elaborate our equation to solve for x, this way:
0.07x + 0.11 (4x + 42,000) = 59,190
0.07x + 0.44x + 4,620 = 59,190
0.51x = 59,190 - 4,620
0.51x = 54,570
x = 54,570/0.51 = 107,000
4. Now we can find the amount the actor invested at 11%, this way:
4x + 42,000 = Money invested at 11%
4 * 107,000 + 42,000 = Money invested at 11%
428,000 + 42,000 = Money invested at 11%
470,000 = Money invested at 11%
5. Let's prove that x = 107,000 is correct, this way:
0.07x + 0.11 (4x + 42,000) = 59,190
0.07 * 107,000 + 0.11 * (4 * 107,000 + 42,000) = 59,190
7,490 + 0.11 * 470,000 = 59,190
7,490 + 51,700 = 59,190
59,190 = 59,190
We proved that x = 107,000 is correct.
6. The answer is that the actor invested $ 107,000 at 7% and $ 470,000 at 11%.
