SOLUTION: Rosie invested $2000 last year. She put some of the money in a 3.5% saving account and the rest in a 5% CD. At the end of the year she earned $84.25 of simple interest from her inv

Algebra ->  Human-and-algebraic-language -> SOLUTION: Rosie invested $2000 last year. She put some of the money in a 3.5% saving account and the rest in a 5% CD. At the end of the year she earned $84.25 of simple interest from her inv      Log On


   



Question 498791: Rosie invested $2000 last year. She put some of the money in a 3.5% saving account and the rest in a 5% CD. At the end of the year she earned $84.25 of simple interest from her investments. HOw much money did Rosie invest in each account?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = amount invested @ 3.5%
Let b = amount invested @ 5%
given:
(1) +a+%2B+b+=+2000+
(2) +.035a+%2B+.05b+=+84.25+
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Multiply both sides of (2) by +1000+
(2) +35a+%2B+50b+=+84250+
Multiply both sides of (1) by +35+
and subtract (1) from (2)
(2) +35a+%2B+50b+=+84250+
(1) +-35a+-+35b+=+-70000+
+15b+=+14250+
+b+=+950+
and, since
(1) +a+%2B+b+=+2000+
(1) +a+%2B+950+=+2000+
(1) +a+=+1050+
$1,050 = amount invested @ 3.5%
$950 = amount invested @ 5%
check:
(2) +.035a+%2B+.05b+=+84.25+
(2) +.035%2A1050+%2B+.05%2A950+=+84.25+
(2) +36.75+%2B+47.5+=+84.25+
(2) +84.25+=+84.25+
OK