$5900 is invested, part of it at 11% and part of it was at 6%. For a certain year, the total yield is at $509.00. How much was invested at each rate?
Let's assume that the amount invested at 11% is x and the amount invested at 6% is $5900 - x.
The interest earned from the investment at 11% is given by 0.11x, and the interest earned from the investment at 6% is given by 0.06($5900 - x).
Given that the total yield is $509.00, we can set up the equation:
0.11x + 0.06($5900 - x) = $509.00
Now, let's solve the equation for x:
0.11x + 0.06($5900 - x) = $509.00
0.11x + $354 - 0.06x = $509.00
0.05x = $509.00 - $354
0.05x = $155.00
x = $155.00 / 0.05
x = $3100.00
So, $3100.00 was invested at 11% and $5900 - $3100.00 = $2800.00 was invested at 6%.
To solve this problem, we'll use a system of equations. Let's denote the amount invested at 11% as "x" and the amount invested at 6% as "5900 - x" (since the total investment is $5900).
The first equation relates the interest earned at 11% to the amount invested at that rate. We know that the interest earned at 11% is calculated by multiplying the amount invested by 0.11 (11% as a decimal). Therefore, the interest earned at 11% would be 0.11x.
The second equation relates the interest earned at 6% to the amount invested at that rate. Similar to the first equation, the interest earned at 6% is calculated by multiplying the amount invested by 0.06 (6% as a decimal). So, the interest earned at 6% would be 0.06(5900 - x).
The total yield is given as $509, so the sum of the interest earned at 11% and 6% should equal $509:
0.11x + 0.06(5900 - x) = 509
To solve this equation, we'll distribute 0.06 to 5900 and -x:
0.11x + 354 - 0.06x = 509
Combining like terms:
0.05x + 354 = 509
Subtracting 354 from both sides of the equation:
0.05x = 155
Dividing both sides by 0.05:
x = 3100
Therefore, $3100 was invested at 11% (x) and the remaining amount, $5900 - $3100 = $2800, was invested at 6% (5900 - x).
if x at 11%, then the rest (5900-x) is at 6%. The interest earned is
0.11x + 0.06(5900-x) = 509.00
x = 3100