you invested 12000 in two accounts paying 5% and 7% annual interest. If the totak interest earned for the year was 760 how much was invested at each rate?
or
amount invested at 5% --- x
amount invested at 7% --- 1200-x
.05x + .07(12000-x) = 760
5x + 7(12000-x) = 76000
-2x = -8000
x = 4000 at 5% , then 12000-4000 or 8000 at 7%
12000*0.05=600
12000*0.07=840
Proportion at 5% = (840-760)/(840-600)=1/3
Proportion at 7% = (760-600)/(840-600)= 2/3 (or 1-1/3=2/3)
(1/3) of 12000 = 4000 at 5%
(2/3) of 12000 = 8000 at 7%
Let's assume you invest x amount of money at 5% interest rate.
Therefore, the amount invested at 7% interest rate will be (12000 - x).
The amount of interest earned from the 5% investment is (x * 0.05) = 0.05x.
The amount of interest earned from the 7% investment is ((12000 - x) * 0.07) = 0.07(12000 - x).
According to the given information, the total interest earned for the year is 760. So, we can set up the equation:
0.05x + 0.07(12000 - x) = 760
Simplifying the equation:
0.05x + 840 - 0.07x = 760
Combining like terms:
-0.02x = -80
Dividing by -0.02:
x = 4000
Therefore, you invested $4000 at 5% interest and the remaining amount, $8000, was invested at 7% interest.
To find out how much was invested at each interest rate, we can set up a system of equations based on the information given.
Let's assume you invested x dollars at a 5% interest rate. This means that the amount invested at a 7% interest rate would be (12000 - x), as the total amount invested is $12000.
We know that the interest earned at a 5% interest rate is given by (x * 0.05), and the interest earned at a 7% interest rate is given by ((12000 - x) * 0.07). The total interest earned is $760.
Setting up the equation:
0.05x + 0.07(12000 - x) = 760
Now, we can solve this equation to find the value of x.
0.05x + 840 - 0.07x = 760
-0.02x = 760 - 840
-0.02x = -80
Dividing both sides of the equation by -0.02:
x = -80 / -0.02
x = 4000
Therefore, you invested $4000 at a 5% interest rate. To find out how much was invested at the 7% interest rate, subtract this amount from the total:
12000 - 4000 = 8000.
So, you invested $4000 at a 5% interest rate and $8000 at a 7% interest rate.