SOLUTION: Brian invested $8000, part in a 5% account and the rest in a 10% account. If his annual interest was $ 650. How much did he invest at each rate?

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Question 553488: Brian invested $8000, part in a 5% account and the rest in a 10% account. If his annual interest was $ 650. How much did he invest at each rate?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = amount invested @ 5%
Let +b+ = amount invested @ 10%
given:
(1) +a+%2B+b+=+8000+
(2) +.05a+%2B+.1b+=+650+
---------------------
(2) +5a+%2B+10b+=+65000+
Multiply both sides of (1) by +5+
and subtract (1) from (2)
(2) +5a+%2B+10b+=+65000+
(1) +-5a+-+5b+=+40000+
+5b+=+25000+
+b+=+5000+
and, since
(1) +a+%2B+b+=+8000+
(1) +a+%2B+5000+=+8000+
(1) +a+=+3000+
He invested $3,000 @ 5% and
$5,000 @ 10%
check answer:
(2) +.05a+%2B+.1b+=+650+
(2) +.05%2A3000+%2B+.1%2A5000+=+650+
(2) +150+%2B+500+=+650+
(2) +650+=+650+
OK