SOLUTION: Erica earned $12,000 last year. He invested part of her money at 3% and the rest at 4% single interest. In one year she earned $440.00 in interest. How much did she invest at each

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Erica earned $12,000 last year. He invested part of her money at 3% and the rest at 4% single interest. In one year she earned $440.00 in interest. How much did she invest at each       Log On

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Question 439570: Erica earned $12,000 last year. He invested part of her money at 3% and the rest at 4% single interest. In one year she earned $440.00 in interest. How much did she invest at each rate
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = amount invested @ 3% interest
Let b = amount invested @ 4% interest
given:
(1) +a+%2B+b+=+12000+
(2) +.03a+%2B+.04b+=+440+
-------------------
(2) +.03a+%2B+.04b+=+440+
(2) +3a+%2B+4b+=+44000+
Multiply both sides of (1) by 3
and subtract (1) from (2)
(2) +3a+%2B+4b+=+44000+
(1) +-3a+-+3b+=+-36000+
+b+=+8000+
and, since
(1) +a+%2B+b+=+12000+
(1) +a+%2B+8000+=+12000+
+a+=+4000+
$4,000 = amount invested @ 3% interest
$8,000 = amount invested @ 4% interest
check answer:
(2) +.03a+%2B+.04b+=+440+
(2) +.03%2A4000+%2B+.04%2A8000+=+440+
+120+%2B+320+=+440+
+440+=+440+
OK