SOLUTION: Phyllis invested 55000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 6 percent per year. After one year the total intere

Algebra ->  Finance -> SOLUTION: Phyllis invested 55000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 6 percent per year. After one year the total intere      Log On


   

Question 1000268: Phyllis invested 55000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 6 percent per year. After one year the total interest earned on these investments was 3090 dollars. How much money did she invest at each rate?
Answer by CountrySLP(2) About Me  (Show Source):
You can put this solution on YOUR website!
X+%2B+Y+=++55000
X+=+55000+-+Y
Y+=+55000+-+X
X+%2A0.05+%2B+Y%2A0.06+=+3090
--Substitute Y in terms of X
X%2A0.05+%2B+%2855000-X%29%2A0.06+=+3090
--Expand the 2nd expression
+%28X%2A0.05%29+%2B+%28%2855000%2A0.06%29-%28X%2A0.06%29%29+=+3090
+%28X%2A0.05%29+%2B+3300+-+%28X%2A0.06%29+=+3090
+%28X%2A0.05%29+-+%28X%2A0.06%29+=+3090+-+3300
+%28X%2A0.05%29-%28X%2A0.06%29+=+-210
--Compress the expression pulling out X
X%280.05-0.06%29+=+-210
X%28-0.01%29+=+-210+
X+=+-210%2F-0.01
X=21000
--Compute Y from X
Y+=+55000+-+X
Y+=+55000+-+21000
Y+=+34000
--Verify the answer
X+%2A0.05+%2B+Y%2A0.06+=+3090
+%2821000%2A0.05%29+%2B+%2834000%2A0.06%29+=+3090
1050+%2B+2040+=+3090 **Correct!