I invested a certain amount of money at 4% and an amount $2000 less than the first amount at 5%. If the income from the 5% investment is 3/4 of the income from the other, find the amount of money that I invested at 4%.
x = amt at 4%
x-2000 = amt at 5%
Now just compare the interest:
.05(x-2000) = .75*.04x
Thank you Steve
To find the amount of money you invested at 4%, let's set up the problem step by step.
Let's assume the amount you invested at 4% is x.
According to the information given, you invested an amount $2000 less than x at 5%. So, the amount invested at 5% would be (x - $2000).
Now, we can calculate the income from each investment.
The income from the 4% investment would be (x * 0.04) = 0.04x.
The income from the 5% investment would be ((x - $2000) * 0.05) = 0.05(x - $2000).
According to the problem, the income from the 5% investment is 3/4 of the income from the 4% investment. So, we can write the equation:
0.05(x - $2000) = (3/4) * 0.04x
To simplify, we can multiply everything by 100 to get rid of the decimals:
5(x - $2000) = 75 * 4x
Now, let's solve for x:
5x - $10000 = 300x
Moving all the x terms to one side and constants to the other side, we have:
300x - 5x = $10000
295x = $10000
Dividing both sides by 295, we get:
x = $10000 / 295
Using a calculator, we can find that x ≈ $33.90 (rounded to two decimal places).
Therefore, the amount of money you invested at 4% is approximately $33.90.