Phyllis invested 55000 dollars, a portion earning a simple interest rate of 4 percent per year and the rest earning a rate of 7 percent per year. After one year the total interest earned on these investments was 2830 dollars. How much money did she invest at each rate?
2380-x= 7%
r=0.07 r=0.04
t=1 t=1
p=x p=2830-x
x(0.07)*1+(2830-x)(0.04)=55000
7x+4.528-0.04x=55000
3x+4.528=55000 / 3x
x=16.824
Please help.
x+y=55000
.04x+.07y=2830
x(0.07)*1+(55000-x)(0.04)=2830
Now solve as you did above.
7x+2,000-4x=2830
3x=5030/3
x=1,676 ?
To solve this problem, we can use the formula for simple interest: interest = principal * rate * time.
Let's assume that Phyllis invested x dollars at a rate of 7% per year. Therefore, the remaining amount she invested, which is 55000 - x dollars, would be invested at a rate of 4% per year.
According to the problem, after one year, the total interest earned on these investments was 2830 dollars. We can now create an equation based on this information:
(x * 0.07 * 1) + ((55000 - x) * 0.04 * 1) = 2830
Simplifying the equation:
0.07x + (2200 - 0.04x) = 2830
Combining like terms:
0.07x - 0.04x + 2200 = 2830
0.03x + 2200 = 2830
Subtracting 2200 from both sides:
0.03x = 630
Dividing both sides by 0.03:
x = 630 / 0.03
Calculating this value:
x = 21000
Therefore, Phyllis invested 21000 dollars at a rate of 7% per year and the remaining amount, 55000 - 21000 = 34000 dollars, at a rate of 4% per year.