Question

Phyllis invested 6500065000 dollars, a portion earning a simple interest rate of 55 percent per year and the rest earning a rate of 77 percent per year. After one year the total interest earned on these investments was 39303930 dollars. How much money did she invest at each rate?
A) At rate 55 percent
B) At rate 77 percent

Answer 1

Let x represent amount invested at 5% and y represent amount invested at 7%.  

We have been given that Phyllis invested 65000, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 7 percent per year. We can represent this information in an equation as:

$x+y=65000...(1)$

$y=65000-x...(1)$

We are also told that after one year the total interest earned on these investments was $3930. We can represent this information in an equation as:

$0.05x+0.07y=3930...(2)$

Upon substituting equation (1) in equation (2), we will get:

$0.05x+0.07(65000-x)=3930$

$0.05x+4550-0.07x=3930$

$-0.02x+4550=3930$

$-0.02x+4550-4550=3930-4550$

$-0.02x=-620$

$\frac{-0.02x}{-0.02}=\frac{-620}{-0.02}$

$x=31000$

Therefore, Phyllis invested $31,000 at 5%.

Upon substituting $x=31000$ in equation (1), we will get:

$y=65000-31000=34000$

Therefore, Phyllis invested $34,000 at 7%.