Sam invested $7000, part at 7% and the rest at 11%. If his total return for one year was $690, how much was invested at each rate?
X * 0.07 + (7000-X) * 0.11 = 690
0.07X + 770 - 0.11X = 690
0.04X = 80
X = 2000 @ 7%
5000 @ 11%
To find out how much Sam invested at each rate, let's assign variables to the unknowns. Let 'x' represent the amount invested at 7% and 'y' represent the amount invested at 11%.
According to the problem, Sam invested a total of $7000, so we have the equation:
x + y = 7000 -------------------(1)
The total return on investment in one year is given as $690. The return on an investment is calculated by multiplying the amount invested by the interest rate. So, we can express the return on the amount invested at 7% as 0.07x and the return on the amount invested at 11% as 0.11y. Therefore, we have the equation:
0.07x + 0.11y = 690 --------------(2)
Now we have a system of equations comprised of equations (1) and (2). We can solve this system of equations to find the values of 'x' and 'y'.
First, let's solve equation (1) for one variable in terms of the other. We can choose to solve for 'x' in terms of 'y':
x = 7000 - y -------------------(3)
Now substitute equation (3) into equation (2) to eliminate 'x':
0.07(7000 - y) + 0.11y = 690
Distribute 0.07 to both terms:
490 - 0.07y + 0.11y = 690
Combine like terms:
0.04y = 200
Divide by 0.04:
y = 5000
Now substitute the value of 'y' back into equation (3) to solve for 'x':
x = 7000 - 5000
x = 2000
Hence, Sam invested $2000 at 7% and $5000 at 11%.