Belinda had $50,000 to invest. She invested part of it at 10% and the remainder at 18%. If her income fromt he two investments was $5,640, then how much did she invest at each rate?
To solve this problem, we can set up a system of equations based on the given information.
Let's assume Belinda invested x amount of dollars at 10% and (50000 - x) amount of dollars at 18%.
The equation for the income from the investment at 10% can be expressed as 0.10x, as 10% of x is the amount earned from that investment.
Similarly, the equation for the income from the investment at 18% can be expressed as 0.18(50000 - x), as 18% of (50000 - x) is the amount earned from that investment.
According to the given information, the total income from the two investments is $5,640. So we can write the equation:
0.10x + 0.18(50000 - x) = 5640
Now let's solve this equation to find the values of x and (50000 - x).
0.10x + 0.18(50000 - x) = 5640
0.10x + 9000 - 0.18x = 5640
-0.08x = 5640 - 9000
-0.08x = -3360
To isolate x, we divide both sides of the equation by -0.08:
x = (-3360) / (-0.08)
x = 42000
So Belinda invested $42,000 at 10% interest rate.
To find out how much she invested at 18%, we subtract this amount from the total investment:
50000 - 42000 = 8000
Belinda invested $8,000 at 18% interest rate.
Therefore, Belinda invested $42,000 at 10% interest rate and $8,000 at 18% interest rate.