Phyllis invested $11,500, a portion earning a simple interest rate of 3 1/5% per year and the rest earning a rate of 3% per year. After one year the total interest earned on these investments was $362.00. How much money did she invest at each rate?

Answer:He invested $8500 with rate 3 1/5% He invested $3000 with rate 3%Step-by-step explanation:* Lets revise the rule of the simple interest- Simple interest I = PRT, where P in the money invested, R is the  interest rate and T is the time of investment- Phyllis invested $11,500- A portion earning a simple interest rate of 3 1/5% (3.2%) per year- The rest earning a rate of 3% per year- After one year the total interest earned on these investments  was $362.00- We need to find the amount of money invested in each rate* Assume that he invested $x with rate 3 1/5% and $y with rate 3%∵ He invested $11,500 in both rates∴ x + y = 11,500 ⇒ (1)∵ He invested $x with 3 1/5%∵ P = $x∵ R = 3.2/100 = 0.032∵ T = 1∴ [tex]I_{1}=x(0.032)(1)[/tex]∴ [tex]I_{1}=0.032x[/tex]∵ He invested $y with 3%∵ P = $y∵ R = 3/100 = 0.03∵ T = 1∴ [tex]I_{2}=y(0.03)(1)[/tex]∴ [tex]I_{2}=0.03y[/tex]∵ The total interest was $362.00- The total interest = [tex]I_{1}[/tex] + [tex]I_{2}[/tex]∴ 0.032x + 0.03y = 362.00 ⇒ (2)We have system of equationsx + y = 11,500 ⇒ (1)0.032x + 0.03y = 362.00 ⇒ (2)Multiply equation (1) by -0.03 to eliminate y-0.03x - 0.03y = 345 ⇒ (3)Add equations (2) and (3)0.002x = 17Divide both sides by 0.002x = 8500Substitute the value of x in equation (1)8500 + y = 11,500Subtract 8500 from both sidesy = 3000* He invested $8500 with rate 3 1/5% * He invested $3000 with rate 3%