A man has $8000 invested, part at 4% and the rest at 2.5 %. The annual income from the 4% investment is $34 more than that from the 2.5% investment. How much is invested at 4%?
If $x is at 4%, the rest $(8000-x) is at 2.5%, so
.04x = .025(8000-x) + 34
Thank you Steve.
To find out how much is invested at 4%, we can set up two equations based on the given information and solve them simultaneously.
Let's assume that the amount invested at 4% is x dollars. Therefore, the amount invested at 2.5% would be (8000 - x) dollars.
We are given that the annual income from the 4% investment is $34 more than that from the 2.5% investment. We can use this information to set up the following equation:
0.04x = 0.025(8000 - x) + 34
In this equation, 0.04x represents the annual income from the 4% investment, and 0.025(8000 - x) represents the annual income from the 2.5% investment plus $34.
Now we can solve this equation to determine the value of x, which represents the amount invested at 4%:
0.04x = 0.025(8000 - x) + 34
0.04x = 200 - 0.025x + 34
0.065x = 234
x = 234 / 0.065
x ≈ 3600
Therefore, approximately $3600 is invested at 4%.